K-theory of cluster C*-algebras
Operator Algebras
2020-09-07 v4 Geometric Topology
Representation Theory
Abstract
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.
Cite
@article{arxiv.1512.00276,
title = {K-theory of cluster C*-algebras},
author = {Igor Nikolaev},
journal= {arXiv preprint arXiv:1512.00276},
year = {2020}
}
Comments
Proceedings of the conference "Quantum Dynamics" in honour of Paul F. Baum on the occasion of his 80th birthday; Banach Center Publications (to appear)