Quantum Cluster Characters

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Title: Quantum Cluster Characters
Author: Rupel, Dylan
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.
URI: http://hdl.handle.net/1794/12400
Date: 2012

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