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arXiv · 2206.03911

The Grothendieck Groups of Discrete Cluster Categories of Dynkin Type $A_{\infty}$

Dave Murphy
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Abstract

In this work we compute the triangulated Grothendieck groups for each of the family of discrete cluster categories of Dynkin type $A_{\infty}$ as introduced by Holm-Jorgensen. Subsequently, we also compute the Grothendieck group of a completion of these discrete cluster categories in the sense of Paquette-Yildirim.

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Dave Murphy. 2022-06-08. The Grothendieck Groups of Discrete Cluster Categories of Dynkin Type $A_{\infty}$. https://arxiv.org/abs/2206.03911

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