Finite group actions on dg categories and Hochschild homology

2024/06/19 by Ville Nordström, Nordstrom, Ville · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2406.13866

openalex publication_date 2024/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a decomposition of the Hochschild homology groups of the equivariant dg category \mathscrC^G associated to a small dg category \mathscrC with direct sums on which a finite group G acts. When the ground field is ℂ this decomposition is related to a categorical action of Rep(G) on \mathscrC^G and the resulting action of the representation ring R_ℂ(G) on HH_\bullet(\mathscrC^G).

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