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## $K$-theory of cluster $C^*$-algebras

### Volume 120 / 2020

Banach Center Publications 120 (2020), 23-34 MSC: 13F60; 46L85. DOI: 10.4064/bc120-2

#### 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 $\mathbb A(1,1)$ coming from triangulation of an annulus with one marked point on each boundary component.

#### Authors

• Igor V. NikolaevDepartment of Mathematics and Computer Science
St. John’s University
8000 Utopia Parkway
New York, NY 11439, U.S.A.
ORCID: 0000-0001-9599-9942
e-mail

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