$\infty$-categorical group quotients via skew group algebras

Fuente: arXiv
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Autore principale: Christ, Merlin
Natura: Preprint
Pubblicazione: 2025
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author Christ, Merlin
author_facet Christ, Merlin
contents We relate group quotients of dg-categories and linear stable $\infty$-categories. Given a group acting on a dg-algebra, we prove that the skew group dg-algebra is Morita equivalent to the dg-categorical homotopy group quotient. We also treat the cases of group actions on dg-categories, with corresponding skew group dg-categories, and of orbit dg-categories. Finally, we describe a version of the skew group algebra in the setting of ring spectra and relate it with $\infty$-categorical group quotients.
format Preprint
id arxiv_https___arxiv_org_abs_2501_13666
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle $\infty$-categorical group quotients via skew group algebras
Christ, Merlin
Representation Theory
Algebraic Topology
18N60, 16E45
We relate group quotients of dg-categories and linear stable $\infty$-categories. Given a group acting on a dg-algebra, we prove that the skew group dg-algebra is Morita equivalent to the dg-categorical homotopy group quotient. We also treat the cases of group actions on dg-categories, with corresponding skew group dg-categories, and of orbit dg-categories. Finally, we describe a version of the skew group algebra in the setting of ring spectra and relate it with $\infty$-categorical group quotients.
title $\infty$-categorical group quotients via skew group algebras
topic Representation Theory
Algebraic Topology
18N60, 16E45
url https://arxiv.org/abs/2501.13666