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Conner, Andrew Brondos, 1981 (University of Oregon, June , 2011)[more][less]Conner, Andrew Brondos, 1981 20110912T19:31:59Z 20130604T17:45:42Z 201106 http://hdl.handle.net/1794/11559 x, 68 p. : ill. (some col.) Motivated by the Adams spectral sequence for computing stable homotopy groups, Priddy defined a class of algebras called Koszul algebras with nice homological properties. Many important algebras arising naturally in mathematics are Koszul, and the Koszul property is often tied to important structure in the settings which produced the algebras. However, the strong defining conditions for a Koszul algebra imply that such algebras must be quadratic. A very natural generalization of Koszul algebras called K 2 algebras was recently introduced by Cassidy and Shelton. Unlike other generalizations of the Koszul property, the class of K 2 algebras is closed under many standard operations in ring theory. The class of K 2 algebras includes ArtinSchelter regular algebras of global dimension 4 on three linear generators as well as graded complete intersections. Our work comprises two distinct projects. Each project was motivated by an aspect of the theory of Koszul algebras which we regard as sufficiently powerful or fundamental to warrant an interpretation for K 2 algebras. A very useful theorem due to Backelin and Fröberg states that if A is a Koszul algebra and I is a quadratic ideal of A which is Koszul as a left A module, then the factor algebra A/I is a Koszul algebra. We prove that if A is Koszul algebra and A I is a K 2 module, then A/I is a K 2 algebra provided A/I acts trivially on Ext A ( A/I,k ). As an application of our theorem, we show that the class of sequentially CohenMacaulay StanleyReisner rings are K 2 algebras and we give examples that suggest the class of K 2 StanleyReisner rings is actually much larger. Another important recent development in ring theory is the use of A ∞ algebras. One can characterize Koszul algebras as those graded algebras whose Yoneda algebra admits only trivial A ∞ structure. We show that, in contrast to the situation for Koszul algebras, vanishing of higher A ∞ structure on the Yoneda algebra of a K 2 algebra need not be determined in any obvious way by the degrees of defining relations. We also demonstrate that obvious patterns of vanishing among higher multiplications cannot detect the K 2 property. This dissertation includes previously unpublished coauthored material. Committee in charge: Dr. Brad Shelton, Chair; Dr. Victor Ostrik, Member; Dr. Nicholas Proudfoot, Member; Dr. Arkady Vaintrob, Member; Dr. David Boush, Outside Member en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2011; Ainfinity Face ring K2 Koszul algebras StanleyReisner Yoneda algebra Ring theory Mathematics A(infinity)structures, generalized Koszul properties, and combinatorial topology Thesis

Fisette, Robert (University of Oregon, 2012)[more][less]Polishchuk, Alexander Fisette, Robert Fisette, Robert 20121026T03:58:22Z 20121026T03:58:22Z 2012 http://hdl.handle.net/1794/12368 We choose a generator G of the derived category of coherent sheaves on a smooth curve X of genus g which corresponds to a choice of g distinguished points P1, . . . , Pg on X. We compute the Hochschild cohomology of the algebra B = Ext (G,G) in certain internal degrees relevant to extending the associative algebra structure on B to an A1structure, which demonstrates that A1structures on B are finitely determined for curves of arbitrary genus. When the curve is taken over C and g = 1, we amend an explicit A1structure on B computed by Polishchuk so that the higher products m6 and m8 become Hochschild cocycles. We use the cohomology classes of m6 and m8 to recover the jinvariant of the curve. When g 2, we use Massey products in Db(X) to show that in the A1structure on B, m3 is homotopic to 0 if and only if X is hyperelliptic and P1, . . . , Pg are chosen to be Weierstrass points. iv en_US University of Oregon All Rights Reserved. Ainfinity Curve Elliptic curve Hochschild cohomology jinvariant The Ainfinity Algebra of a Curve and the Jinvariant Electronic Thesis or Dissertation

Bibby, Christin (University of Oregon, August 18, 2015)[more][less]Proudfoot, Nicholas Bibby, Christin 20150818T23:04:51Z 20150818T23:04:51Z 20150818 http://hdl.handle.net/1794/19273 An abelian arrangement is a finite set of codimension one abelian subvarieties (possibly translated) in a complex abelian variety. We are interested in the topology of the complement of an arrangement. If the arrangement is unimodular, we provide a combinatorial presentation for a differential graded algebra (DGA) that is a model for the complement, in the sense of rational homotopy theory. Moreover, this DGA has a bigrading that allows us to compute the mixed Hodge numbers. If the arrangement is chordal, then this model is a Koszul algebra. In this case, studying its quadratic dual gives a combinatorial description of the Qnilpotent completion of the fundamental group and the minimal model of the complement of the arrangement. This dissertation includes previously unpublished coauthored material. en_US University of Oregon All Rights Reserved. hyperplane arrangements Abelian Arrangements Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Loubert, Joseph (University of Oregon, August 18, 2015)[more][less]Kleshchev, Alexander Loubert, Joseph 20150818T23:02:53Z 20150818T23:02:53Z 20150818 http://hdl.handle.net/1794/19255 This thesis consists of two parts. In the first we prove that the KhovanovLaudaRouquier algebras $R_\alpha$ of finite type are (graded) affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger property, namely that the affine cell ideals in $R_\alpha$ are generated by idempotents. This in particular implies the (known) result that the global dimension of $R_\alpha$ is finite. In the second part we use the presentation of the Specht modules given by KleshchevMathasRam to derive results about Specht modules. In particular, we determine all homomorphisms from an arbitrary Specht module to a fixed Specht module corresponding to any hook partition. Along the way, we give a complete description of the action of the standard KLR generators on the hook Specht module. This work generalizes a result of James. This dissertation includes previously published coauthored material. en_US University of Oregon All Rights Reserved. Affine Cellularity KLR Algebras Specht Modules Affine Cellularity of Finite Type KLR Algebras, and Homomorphisms Between Specht Modules for KLR Algebras in Affine Type A Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Schultz, Patrick (University of Oregon, September 29, 2014)[more][less]Dugger, Daniel Schultz, Patrick 20140929T17:53:19Z 20140929 http://hdl.handle.net/1794/18429 We present a generalized framework for the theory of algebraic weak factorization systems, building on work by Richard Garner and Emily Riehl. We define cyclic 2fold double categories, and bimonads (or bialgebras) and lax/colax bimonad morphisms inside cyclic 2fold double categories. After constructing a cyclic 2fold double category <bold>FF</bold>(D) of functorial factorization systems in any sufficiently nice 2category D, we show that bimonads and lax/colax bimonad morphsims in <bold>FF</bold>(Cat) agree with previous definitions of algebraic weak factorization systems and lax/colax morphisms. We provide a proof of one of the core technical theorems from previous work on algebraic weak factorization systems in our generalized framework. Finally, we show that this framework can be further generalized to cyclic 2fold double multicategories, incorporating Quillen functors of several variables. en_US University of Oregon All Rights Reserved. Category Theory Double Categories Model Categories Algebraic Weak Factorization Systems in Double Categories Electronic Thesis or Dissertation 20160929 Ph.D. doctoral Department of Mathematics University of Oregon

Ro, Min (University of Oregon, August 18, 2015)[more][less]Lin, Huaxin Ro, Min 20150818T22:52:07Z 20150818T22:52:07Z 20150818 http://hdl.handle.net/1794/19199 In this dissertation, we explore the approximate diagonalization of unital homomorphisms between C*algebras. In particular, we prove that unital homomorphisms from commutative C*algebras into simple separable unital C*algebras with tracial rank at most one are approximately diagonalizable. This is equivalent to the approximate diagonalization of commuting sets of normal matrices. We also prove limited generalizations of this theorem. Namely, certain injective unital homomorphisms from commutative C*algebras into simple separable unital C*algebras with rational tracial rank at most one are shown to be approximately diagonalizable. Also unital injective homomorphisms from AHalgebras with unique tracial state into separable simple unital C*algebras of tracial rank at most one are proved to be approximately diagonalizable. Counterexamples are provided showing that these results cannot be extended in general. Finally, we prove that for unital homomorphisms between AFalgebras, approximate diagonalization is equivalent to a combinatorial problem involving sections of lattice points in cones. en_US University of Oregon All Rights Reserved. approximate diagonalization C*algebras Elliott classification Approximate Diagonalization of Homomorphisms Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Comes, Jonathan, 1981 (University of Oregon, June , 2010)[more][less]Comes, Jonathan, 1981 20101203T20:42:43Z 20101203T20:42:43Z 201006 http://hdl.handle.net/1794/10867 x, 81 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. We give an exposition of Deligne's tensor category Rep(St) where t is not necessarily an integer. Thereafter, we give a complete description of the blocks in Rep(St) for arbitrary t. Finally, we use our result on blocks to decompose tensor products and classify tensor ideals in Rep(St). Committee in charge: Victor Ostrik, Chairperson, Mathematics; Daniel Dugger, Member, Mathematics; Jonathan Brundan, Member, Mathematics; Alexander Kleshchev, Member, Mathematics; Michael Kellman, Outside Member, Chemistry en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Tensor category Symmetric groups Decomposed blocks Tensor products Tensor ideals Mathematics Theoretical mathematics Blocks in Deligne's category Rep(St) Thesis

Davidson, Nicholas (University of Oregon, November 21, 2016)[more][less]Brundan, Jonathan Davidson, Nicholas 20161121T16:58:19Z 20161121T16:58:19Z 20161121 http://hdl.handle.net/1794/20704 This dissertation uses techniques from the theory of categorical actions of KacMoody algebras to study the analog of the BGG category O for the queer Lie superalgebra. Chen recently reduced many questions about this category to its socalled types A, B, and C blocks. The type A blocks were completely described in joint work with Brundan in terms of the general linear Lie superalgebra. This dissertation proves that the type C blocks admit the structure of a tensor product categorification of the nfold tensor power of the natural sp_\inftymodule. Using this result, we relate the combinatorics for these blocks to Webster’s orthodox bases for the quantum group of type C_\infty, verifying the truth of a recent conjecture of ChengKwonWang. This dissertation contains coauthored material. en_US University of Oregon All Rights Reserved. Categorification KacMoody Representation Theory Superalgebra Supercategorification Supercategory Categorical Actions on Supercategory O Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Platt, David (University of Oregon, October 3, 2013)[more][less]Polishchuk, Alexander Platt, David 20131003T23:32:01Z 20131003T23:32:01Z 20131003 http://hdl.handle.net/1794/13244 We give a formula for the Chern character on the DG category of global matrix factorizations on a smooth scheme $X$ with superpotential $w\in \Gamma(\O_X)$. Our formula takes values in a Cech model for Hochschild homology. Our methods may also be adapted to get an explicit formula for the Chern character for perfect complexes of sheaves on $X$ taking values in right derived global sections of the DeRham algebra. Along the way we prove that the DG version of the Chern Character coincides with the classical one for perfect complexes. en_US University of Oregon All Rights Reserved. Chern Character Matrix Factorizations Noncommutative Geometry Chern Character for Global Matrix Factorizations Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Pearson, Kelly Jeanne, 1970 (2000)[more][less]Pearson, Kelly Jeanne, 1970 20080210T03:23:05Z 20080210T03:23:05Z 2000 0599841095 http://hdl.handle.net/1794/141 vii, 91 p. A print copy of this title is available through the UO Libraries under the call number: MATH QC20.7.H65 P43 2000 The OrlikSolomon algebra of a hyperplane arrangement first appeared from the Brieskorn and OrlikSolomon theorems as the cohomology of the complement of this arrangement (if the ground field is complex). Later, it was discovered that this algebra plays an important role in many other problems. In particular, define the cohomology of an OrlikSolomon algebra as that of the complex formed by its homogeneous components with the differential defined via multiplication by an element of degree one. Cohomology of the OrlikSolomon algebra is mostly studied in dimension one, and very little is known about the higher dimensions. We study this cohomology in higher dimensions. Adviser: Sergey Yuzvinsky. 3856498 bytes 122293 bytes 1483 bytes application/pdf text/plain text/plain en University of Oregon theses, Dept. of Mathematics, Ph. D., 2000 Cohomology operations Homology theory Cohomology of the OrlikSolomon algebras Thesis

Gardella, Eusebio (University of Oregon, August 18, 2015)[more][less]Phillips, N. Christopher Gardella, Eusebio 20150818T23:13:52Z 20150818T23:13:52Z 20150818 http://hdl.handle.net/1794/19345 This dissertation is concerned with representations of locally compact groups on different classes of Banach spaces. The first part of this work considers representations of compact groups by automorphisms of C*algebras, also known as group actions on C*algebras. The actions we study enjoy a freenesstype of property, namely finite Rokhlin dimension. We investigate the structure of their crossed products, mainly in relation to their classifiability, and compare the notion of finite Rokhlin dimension with other existing notions of noncommutative freeness. In the case of Rokhlin dimension zero, also known as the Rokhlin property, we prove a number of classification theorems for these actions. Also, in this case, much more can be said about the structure of the crossed products. In the last chapter of this part, we explore the extent to which actions with Rokhlin dimension one can be classified. Our results show that even for Z_2actions on O_2, their classification is not Borel, and hence it is intractable. The second part of the present dissertation focuses on isometric representations of groups on Lpspaces. For p=2, these are the unitary representations on Hilbert spaces. We study the Lpanalogs of the full and reduced group \ca s, particularly in connection to their rigidity. One of the main results of this work asserts that for p different from 2, the isometric isomorphism type of the reduced group Lpoperator algebra recovers the group. Our study of group algebras acting on Lpspaces has also led us to answer a 20yearold question of Le Merdy and Junge: for p different from 2, the class of Banach algebras that can be represented on an Lpspace is not closed under quotients. We moreover study representations of groupoids, which are a generalization of groups where multiplication is not always defined. The algebras associated to these objects provide new examples of Lpoperator algebras and recover some previously existing ones. Groupoid Lpoperator algebras are particularly tractable objects. For instance, while groupoid Lpoperator algebras can be classified by their K_0group (an ordered, countable abelian group), we show that UHFLpoperator algebras not arising from groupoids cannot be classified by countable structures. This dissertation includes unpublished coauthored material. en_US University of Oregon All Rights Reserved. C*algebras Classification Cossed product Group action Lpspace ppseudofunctions Compact Group Actions on C*algebras: Classification, NonClassifiability and Crossed Products and Rigidity Results for Lpoperator Algebras Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Archey, Dawn Elizabeth, 1979 (University of Oregon, June , 2008)[more][less]Archey, Dawn Elizabeth, 1979 20081220T02:10:58Z 20081220T02:10:58Z 200806 http://hdl.handle.net/1794/8155 viii, 107 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. This dissertation consists of two related parts. In the first portion we use the tracial Rokhlin property for actions of a finite group G on stably finite simple unital C *algebras containing enough projections. The main results of this part of the dissertation are as follows. Let A be a stably finite simple unital C *algebra and suppose a is an action of a finite group G with the tracial Rokhlin property. Suppose A has real rank zero, stable rank one, and suppose the order on projections over A is determined by traces. Then the crossed product algebra C * ( G, A, Ã Ã Â±) also has these three properties. In the second portion of the dissertation we introduce an analogue of the tracial Rokhlin property for C *algebras which may not have any nontrivial projections called the projection free tracial Rokhlin property . Using this we show that under certain conditions if A is an infinite dimensional simple unital C *algebra with stable rank one and Ã Ã Â± is an action of a finite group G with the projection free tracial Rokhlin property, then C * ( G, A, Ã Ã Â±) also has stable rank one. Adviser: Phillips, N. Christopher en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph.D., 2008; Mathematics Cuntz subequivalence Stable rank one Tracial Rokhlin property Finite group actions Crossed product C*algebras Crossed product C*algebras by finite group actions with a generalized tracial Rokhlin property Thesis

Crossed product C*algebras of certain nonsimple C*algebras and the tracial quasiRokhlin propertyBuck, Julian Michael, 1982 (University of Oregon, June , 2010)[more][less]Buck, Julian Michael, 1982 20101130T23:48:55Z 20101130T23:48:55Z 201006 http://hdl.handle.net/1794/10849 viii, 113 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. This dissertation consists of four principal parts. In the first, we introduce the tracial quasiRokhlin property for an automorphism α of a C *algebra A (which is not assumed to be simple or to contain any projections). We then prove that under suitable assumptions on the algebra A , the associated crossed product C *algebra C *([Special characters omitted.] , A , α) is simple, and the restriction map between the tracial states of C *([Special characters omitted.] , A , α) and the αinvariant tracial states on A is bijective. In the second part, we introduce a comparison property for minimal dynamical systems (the dynamic comparison property) and demonstrate sufficient conditions on the dynamical system which ensure that it holds. The third part ties these concepts together by demonstrating that given a minimal dynamical system ( X, h ) and a suitable simple C *algebra A , a large class of automorphisms β of the algebra C ( X, A ) have the tracial quasiRokhlin property, with the dynamic comparison property playing a key role. Finally, we study the structure of the crossed product C *algebra B = C *([Special characters omitted.] , C ( X , A ), β) by introducing a subalgebra B { y } of B , which is shown to be large in a sense that allows properties B { y } of to pass to B . Several conjectures about the deeper structural properties of B { y } and B are stated and discussed. Committee in charge: Christopher Phillips, Chairperson, Mathematics; Daniel Dugger, Member, Mathematics; Huaxin Lin, Member, Mathematics; Marcin Bownik, Member, Mathematics; Van Kolpin, Outside Member, Economics en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Dynamical systems Minimal homeomorphisms Crossed product algebras Tracial property Automorphisms C*algebras QuasiRokhlin property Mathematics Theoretical mathematics Crossed product C*algebras of certain nonsimple C*algebras and the tracial quasiRokhlin property Thesis

Sun, Wei, 1979 (University of Oregon, June , 2010)[more][less]Sun, Wei, 1979 20101222T01:32:21Z 20101222T01:32:21Z 201006 http://hdl.handle.net/1794/10912 vii, 124 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. This dissertation is a study of the relationship between minimal dynamical systems on the product of the Cantor set ( X ) and torus ([Special characters omitted]) and their corresponding crossed product C *algebras. For the case when the cocyles are rotations, we studied the structure of the crossed product C *algebra A by looking at a large subalgebra A x . It is proved that, as long as the cocyles are rotations, the tracial rank of the crossed product C *algebra is always no more than one, which then indicates that it falls into the category of classifiable C *algebras. In order to determine whether the corresponding crossed product C *algebras of two such minimal dynamical systems are isomorphic or not, we just need to look at the Elliott invariants of these C *algebras. If a certain rigidity condition is satisfied, it is shown that the crossed product C *algebra has tracial rank zero. Under this assumption, it is proved that for two such dynamical systems, if A and B are the corresponding crossed product C *algebras, and we have an isomorphism between K i ( A ) and K i ( B ) which maps K i (C(X ×[Special characters omitted])) to K i (C( X ×[Special characters omitted])), then these two dynamical systems are approximately K conjugate. The proof also indicates that C *strongly flip conjugacy implies approximate K conjugacy in this case. We also studied the case when the cocyles are Furstenberg transformations, and some results on weakly approximate conjugacy and the K theory of corresponding crossed product C *algebras are obtained. Committee in charge: Huaxin Lin, Chairperson, Mathematics Daniel Dugger, Member, Mathematics; Christopher Phillips, Member, Mathematics; Arkady Vaintrob, Member, Mathematics; LiShan Chou, Outside Member, Human Physiology en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Tracial rank Approximate conjugacy C*algebras Minimal dynamical systems Cantor set Torus Mathematics Theoretical mathematics Crossed product C*algebras of minimal dynamical systems on the product of the Cantor set and the torus Thesis

Liang, Hutian (University of Oregon, June , 2010)[more][less]Liang, Hutian 20110114T18:44:40Z 20110114T18:44:40Z 201006 http://hdl.handle.net/1794/10938 viii, 133 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. In this dissertation, we will study the crossed product C*algebras obtained from free and minimal [Special characters omitted.] actions on compact metric spaces with finite covering dimension. We first define stable recursive subhomogeneous algebras (SRSHAs), which differ from recursive subhomogeneous algebras introduced by N. C. Phillips in that the irreducible representations of SRSHAs are infinite dimensional instead of finite dimensional. We show that simple inductive limits of SRSHAs with no dimension growth in which the connecting maps are injective and nonvanishing have topological stable rank one. We then construct C*subalgebras of the crossed product that are analogous to the C*subalgebras in the studies of free minimal [Special characters omitted.] actions on compact metric spaces with finite covering dimension. Finally, we prove that these C*algebras are in fact simple inductive limits of SRSHAs in which the connecting maps are injective and nonvanishing. Thus these C*subalgebras have topological stable rank one. Committee in charge: Christopher Phillips, Chairperson, Mathematics; Boris Botvinnik, Member, Mathematics; Huaxin Lin, Member, Mathematics; Yuan Xu, Member, Mathematics; Dietrich Belitz, Outside Member, Physics en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Free minimal action Metric space Subhomogeneous algebras Infinite dimensions Topological stability Mathematics Theoretical mathematics The crossed product of C(X) by a free minimal action of R Thesis

Chettih, Safia (University of Oregon, November 21, 2016)[more][less]Sinha, Dev Chettih, Safia 20161121T17:00:59Z 20161121T17:00:59Z 20161121 http://hdl.handle.net/1794/20728 We prove that the nonkequal configuration space of a graph has a discretized model, analogous to the discretized model for configurations on graphs. We apply discrete Morse theory to the latter to give an explicit combinatorial formula for the ranks of homology and cohomology of configurations of two points on a tree. We give explicit presentations for homology and cohomology classes as well as pairings for ordered and unordered configurations of two and three points on a few simple trees, and show that the first homology group of ordered and unordered configurations of two points in any tree is generated by the first homology groups of configurations of two points in three particular graphs, K_{1,3}, K_{1,4}, and the trivalent tree with 6 vertices and 2 vertices of degree 3, via graph embeddings. en_US University of Oregon All Rights Reserved. configuration space discrete Morse theory graph braid group nonkequal configuration Dancing in the Stars: Topology of Nonkequal Configuration Spaces of Graphs Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Brown, Jonathan, 1975 (University of Oregon, June , 2009)[more][less]Brown, Jonathan, 1975 20100219T01:28:27Z 20100219T01:28:27Z 200906 http://hdl.handle.net/1794/10201 ix, 114 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. In this work we prove that the finite W algebras associated to nilpotent elements in the symplectic or orthogonal Lie algebras whose Jordan blocks are all the same size are quotients of twisted Yangians. We use this to classify the finite dimensional irreducible representations of these finite W algebras. Committee in charge: Jonathan Brundan, CoChairperson, Mathematics; Victor Ostrik, CoChairperson, Mathematics; Arkady Berenstein, Member, Mathematics; Hal Sadofsky, Member, Mathematics; Christopher Wilson, Outside Member, Computer & Information Science en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2009; Finite Walgebras Nilpotent Symplectic Quantum algebra Mathematics Walgebras Finite Walgebras of classical type Thesis

Iverson, Joseph (University of Oregon, October 27, 2016)[more][less]Bownik, Marcin Iverson, Joseph 20161027T18:36:03Z 20161027T18:36:03Z 20161027 http://hdl.handle.net/1794/20443 Let $G$ be a second countable, locally compact group which is either compact or abelian, and let $\rho$ be a unitary representation of $G$ on a separable Hilbert space $\mathcal{H}_\rho$. We examine frames of the form $\{ \rho(x) f_j \colon x \in G, j \in I\}$ for families $\{f_j\}_{j \in I}$ in $\mathcal{H}_\rho$. In particular, we give necessary and sufficient conditions for the joint orbit of a family of vectors in $\mathcal{H}_\rho$ to form a continuous frame. We pay special attention to this problem in the setting of shift invariance. In other words, we fix a larger second countable locally compact group $\Gamma \supset G$ containing $G$ as a closed subgroup, and we let $\rho$ be the action of $G$ on $L^2(\Gamma)$ by left translation. In both the compact and the abelian settings, we introduce notions of Zak transforms on $L^2(\Gamma)$ which simplify the analysis of group frames. Meanwhile, we run a parallel program that uses the Zak transform to classify closed subspaces of $L^2(\Gamma)$ which are invariant under left translation by $G$. The two projects give compatible outcomes. This dissertation contains previously published material. en_US University of Oregon All Rights Reserved. compact group dual integrable group frame LCA group shiftinvariant Zak transform Frames Generated by Actions of Locally Compact Groups Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Thornton, Josiah (University of Oregon, 2012)[more][less]Ostrik, Victor Thornton, Josiah Thornton, Josiah 20121026T04:06:42Z 20121026T04:06:42Z 2012 http://hdl.handle.net/1794/12450 We give an exposition of neargroup categories and generalized neargroup categories. We show that both have a pseudounitary structure. We complete the classification of braided neargroup categories and discuss the inherent structures on both symmetric and modular generalized neargroup categories. en_US University of Oregon All Rights Reserved. Generalized NearGroup Categories Electronic Thesis or Dissertation

Heuser, Aaron, 1978 (University of Oregon, June , 2010)[more][less]Heuser, Aaron, 1978 20101203T22:34:13Z 20101203T22:34:13Z 201006 http://hdl.handle.net/1794/10870 x, 110 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. This dissertation examines the existence of the selfintersection local time for a superprocess over a stochastic flow in dimensions d ≤ 3, which through constructive methods, gives a Tanaka like representation. The superprocess over a stochastic flow is a superprocess with dependent spatial motion, and thus Dynkin's proof of existence, which requires multiplicity of the logLaplace functional, no longer applies. Skoulakis and Adler's method of calculating moments is extended to higher moments, from which existence follows. Committee in charge: Hao Wang, CoChairperson, Mathematics; David Levin, CoChairperson, Mathematics; Christopher Sinclair, Member, Mathematics; Huaxin Lin, Member, Mathematics; Van Kolpin, Outside Member, Economics en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Selfintersection Tanaka representation Superprocess Stochastic flow Mathematics Theoretical mathematics Generalized selfintersection local time for a superprocess over a stochastic flow Thesis
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