The Grothendieck groups of n-cluster categories of type A_{\infty}

Huimin Chang

paper

The Grothendieck groups of n-cluster categories of type A_{\infty}

arXiv:2509.20661

Abstract

In this article, we investigate the Grothendieck groups $K_0(\C_{A_{\infty}}^n)$ of $n$ -cluster categories $\C_{A_{\infty}}^n$ of type $A_{\infty}$ introduced by T.~Holm and P.~Jørgensen. We prove that $K_0(\C_{A_{\infty}}^n)\cong\mathbb{Z}$ for an arbitrary $n \geq 1$ . As an application, this generalizes a result of Murphy for $n = 1$ .