Metric completions of discrete cluster categories

2024/07/24 by Cummings, Charley, Gratz, Sira · 4 citations
#18G80 #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2407.17369

Abstract

Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In particular, for a coaisle metric this yields a new triangulated category which can be interpreted as a topological completion of the associated combinatorial model. Moreover, we show that the completion of any triangulated category with respect to an internal aisle metric is a thick subcategory of the triangulated category itself.

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• An equivalence linking CM-types A_∞ and D_∞
• Metric completions of triangulated categories from hereditary rings
• Negative Calabi-Yau discrete cluster categories via Nakayama representations and persistence theory
• Ind-cluster algebras and infinite Grassmannians

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