The Grothendieck Groups of Discrete Cluster Categories of Dynkin Type A_∞

2022/06/08 by Murphy, Dave · 3 citations
#Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2206.03911

Abstract

In this work we compute the triangulated Grothendieck groups for each of the family of discrete cluster categories of Dynkin type A_∞ 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.

Cited by

• Triangulated Categories Admitting Linear Generators
• The Grothendieck groups of n-cluster categories of type A_∞
• Negative Calabi-Yau discrete cluster categories via Nakayama representations and persistence theory

Related

• The Grothendieck groups of n-cluster categories of type A_∞
• The Grothendieck group of a triangulated category
• Grothendieck groups of repetitive cluster categories
• Theorie homotopique des DG-categories
• Continuous cluster categories of type D