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Quantum Cluster Characters

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.

Identiferoai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/12400
Date January 2012
CreatorsRupel, Dylan, Rupel, Dylan
ContributorsBerenstein, Arkady
PublisherUniversity of Oregon
Source SetsUniversity of Oregon
Languageen_US
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
RightsAll Rights Reserved.

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