Finite group actions on dg categories and Hochschild homology

Ville Nordstrom
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Abstract

We prove a decomposition of the Hochschild homology groups of the equivariant dg category $\mathscr{C}^G$ associated to a small dg category $\mathscr{C}$ with direct sums on which a finite group $G$ acts. When the ground field is $\mathbb{C}$ this decomposition is related to a categorical action of $\text{Rep}(G)$ on $\mathscr{C}^G$ and the resulting action of the representation ring $R_\mathbb{C}(G)$ on $HH_\bullet(\mathscr{C}^G)$.
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dg 类上的有限群作用与霍赫希尔德同源性
我们证明了等价dg范畴$\mathscr{C}^G$的霍赫希尔德同调群的分解,这个等价dg范畴与有限群$G$作用的有直接和的小dg范畴$\mathscr{C}$相关联。当基域是$mathbb{C}$时,这种分解与$text{Rep}(G)$在$mathscr{C}^G$上的分类作用以及由此产生的呈现环$R_\mathbb{C}(G)$在$H_\bullet(\mathscr{C}^G)$上的作用有关。
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