Hochschild cohomology of the second kind: Koszul duality and Morita invariance
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866908840806580224 |
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| author | Guan, Ai Holstein, Julian Lazarev, Andrey |
| author_facet | Guan, Ai Holstein, Julian Lazarev, Andrey |
| contents | We define Hochschild cohomology of the second kind for differential graded (dg) or curved algebras as a derived functor in the twisted derived category, and show that it is invariant under suitable Morita equivalences of the second kind. A bimodule version of Koszul duality is constructed and used to show that Hochschild cohomology of the second kind is preserved under (nonconilpotent) Koszul duality. We show that Hochschild cohomology of the second kind of an algebra often computes the ordinary Hochschild cohomology of geometrically meaningful dg categories. Examples include the category of infinity local systems on a topological space, the bounded derived category of a complex algebraic manifold and the category of matrix factorizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16645 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hochschild cohomology of the second kind: Koszul duality and Morita invariance Guan, Ai Holstein, Julian Lazarev, Andrey Category Theory Algebraic Geometry Algebraic Topology We define Hochschild cohomology of the second kind for differential graded (dg) or curved algebras as a derived functor in the twisted derived category, and show that it is invariant under suitable Morita equivalences of the second kind. A bimodule version of Koszul duality is constructed and used to show that Hochschild cohomology of the second kind is preserved under (nonconilpotent) Koszul duality. We show that Hochschild cohomology of the second kind of an algebra often computes the ordinary Hochschild cohomology of geometrically meaningful dg categories. Examples include the category of infinity local systems on a topological space, the bounded derived category of a complex algebraic manifold and the category of matrix factorizations. |
| title | Hochschild cohomology of the second kind: Koszul duality and Morita invariance |
| topic | Category Theory Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2312.16645 |