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.
| Identifer | oai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/12400 |
| Date | January 2012 |
| Creators | Rupel, Dylan, Rupel, Dylan |
| Contributors | Berenstein, Arkady |
| Publisher | University of Oregon |
| Source Sets | University of Oregon |
| Language | en_US |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Rights | All Rights Reserved. |
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