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 $HH_\bullet (\mathscr {C}^G)$.
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
@article{10_4153_S000843952500030X,
author = {Nordstr\"om, Ville},
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/}
}
TY - JOUR AU - Nordström, Ville TI - Finite group actions on dg categories and Hochschild homology JO - Canadian mathematical bulletin PY - 2025 SP - 1088 EP - 1108 VL - 68 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/S000843952500030X/ DO - 10.4153/S000843952500030X ID - 10_4153_S000843952500030X ER -
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