June 19, 2024Open Access

Finite group actions on dg categories and Hochschild homology

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Abstract

We prove a decomposition of the Hochschild homology groups of the equivariant dg category CG associated to a small dg category C 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 CG and the resulting action of the representation ring RC (G) on HH_ (CG).

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Ville Nordström (Wed,) studied this question.

synapsesocial.com/papers/68e64297b6db6435875d44e0 https://doi.org/https://doi.org/10.48550/arxiv.2406.13866

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