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 relate...
Main Author: | |
---|---|
Other Authors: | |
Language: | en_US |
Published: |
University of Oregon
2012
|
Subjects: | |
Online Access: | http://hdl.handle.net/1794/12400 |
Summary: | 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. |
---|