Quantum Cluster Characters

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...

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Bibliographic Details
Main Author: Rupel, Dylan
Other Authors: Berenstein, Arkady
Language:en_US
Published: University of Oregon 2012
Subjects:
Cluster
Quantum
Quiver
Tilting
Online Access:http://hdl.handle.net/1794/12400
id ndltd-uoregon.edu-oai-scholarsbank.uoregon.edu-1794-12400
record_format oai_dc
spelling ndltd-uoregon.edu-oai-scholarsbank.uoregon.edu-1794-124002018-12-20T05:48:01Z Quantum Cluster Characters Rupel, Dylan Rupel, Dylan Berenstein, Arkady Cluster Quantum Quiver Tilting 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. 2012-10-26T04:01:34Z 2012-10-26T04:01:34Z 2012 Electronic Thesis or Dissertation http://hdl.handle.net/1794/12400 en_US All Rights Reserved. University of Oregon
collection NDLTD
language en_US
sources NDLTD
topic Cluster
Quantum
Quiver
Tilting
spellingShingle Cluster
Quantum
Quiver
Tilting
Rupel, Dylan
Rupel, Dylan
Quantum Cluster Characters
description 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.
author2 Berenstein, Arkady
author_facet Berenstein, Arkady
Rupel, Dylan
Rupel, Dylan
author Rupel, Dylan
Rupel, Dylan
author_sort Rupel, Dylan
title Quantum Cluster Characters
title_short Quantum Cluster Characters
title_full Quantum Cluster Characters
title_fullStr Quantum Cluster Characters
title_full_unstemmed Quantum Cluster Characters
title_sort quantum cluster characters
publisher University of Oregon
publishDate 2012
url http://hdl.handle.net/1794/12400
work_keys_str_mv AT rupeldylan quantumclustercharacters
AT rupeldylan quantumclustercharacters
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