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Finite group actions on dg categories and Hochschild homology
Published online by Cambridge University Press: 17 March 2025
Abstract
Let G be a finite group whose order is not divisible by the characteristic of the ground field 
$\mathbb {F}$. We prove a decomposition of the Hochschild homology groups of the equivariant dg category 
$\mathscr {C}^G$ associated with the action of G on a small dg category 
$\mathscr {C}$ which admits finite direct sums. When, in addition, the ground field 
$\mathbb {F}$ is algebraically closed this decomposition is related to a categorical action of 
$\text {Rep}(G)$ on 
$\mathscr {C}^G$ and the resulting action of the representation ring 
$R_{\mathbb {F}}(G)$ on 
$HH_\bullet (\mathscr {C}^G)$.
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- © The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society
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