Finite group actions on dg categories and Hochschild homology
Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1088-1108

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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 $HH_\bullet (\mathscr {C}^G)$.
DOI : 10.4153/S000843952500030X
Mots-clés : Hochschild homology, dg categories, group actions
Nordström, Ville. Finite group actions on dg categories and Hochschild homology. Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1088-1108. doi: 10.4153/S000843952500030X
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     title = {Finite group actions on dg categories and {Hochschild} homology},
     journal = {Canadian mathematical bulletin},
     pages = {1088--1108},
     year = {2025},
     volume = {68},
     number = {4},
     doi = {10.4153/S000843952500030X},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S000843952500030X/}
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