Quantum Cluster Characters
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Date
2012
Authors
Rupel, Dylan
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
We de ne the quantum cluster character assigning an element of a quantum torus to each
representation of a valued quiver (Q; d) and investigate its relationship to external and internal
mutations of a quantum cluster algebra associated to (Q; d). We will see that the external mutations
are related to re
ection functors and internal mutations are related to tilting theory. Our
main result will show the quantum cluster character gives a cluster monomial in this quantum
cluster algebra whenever the representation is rigid, moreover we will see that each non-initial
cluster variable can be obtained in this way from the quantum cluster character.
Description
Keywords
Cluster, Quantum, Quiver, Tilting