Browsing by Subject "Quantum algebra"

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Finite W-algebras of classical type

Brown, Jonathan, 1975- (University of Oregon, 2009-06)

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 ...
Relations in the Witt Group of Nondegenerate Braided Fusion Categories Arising from the Representation Theory of Quantum Groups at Roots of Unity

Schopieray, Andrew (University of Oregon, 2017-09-06)

For each finite dimensional Lie algebra $\mathfrak{g}$ and positive integer $k$ there exists a modular tensor category $\mathcal{C}(\mathfrak{g},k)$ consisting of highest weight integrable $\hat{\mathfrak{g}}$-modules of ...