K-theory of cluster C-algebras

It is proved that the K_0-group of a cluster C*-algebra is isomorphic to the corresponding cluster algebra. As a corollary, one gets a shorter proof of the positivity conjecture for cluster algebras. As an example, we consider a cluster C*-algebra A(1,1) coming from triangulation of an annulus with...

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Veröffentlicht in:	arXiv.org 2018-10
1. Verfasser:	Nikolaev, Igor
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Clusters Mathematics - Geometric Topology Mathematics - Operator Algebras Mathematics - Representation Theory Triangulation
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Zusammenfassung:	It is proved that the K_0-group of a cluster C-algebra is isomorphic to the corresponding cluster algebra. As a corollary, one gets a shorter proof of the positivity conjecture for cluster algebras. As an example, we consider a cluster C-algebra A(1,1) coming from triangulation of an annulus with one marked point on each boundary component.
ISSN:	2331-8422
DOI:	10.48550/arxiv.1512.00276