$\infty$-categorical group quotients via skew group algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913014038396928 |
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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 |