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| Format: | Preprint |
| Publié: |
2021
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| Accès en ligne: | https://arxiv.org/abs/2111.01735 |
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| _version_ | 1866917738288513024 |
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| author | Sarkar, Abhishek |
| author_facet | Sarkar, Abhishek |
| contents | We consider Lie algebroids over an algebraic space (or topological ringed space) as quasicoherent sheaves of Lie-Rinehart algebras. We express hypercohomology for a locally free Lie algebroid (not necessarily of finite rank) as a derived functor, and simplify it via Čech cohomology. Furthermore, we define the Hochschild hypercohomology of a sheaf of generalized bialgebras and study the cases of the universal enveloping algebroid and the jet algebroid of a Lie algebroid. In the sequel, we present a version of Hochschild-Kostant-Rosenberg theorem for a locally free Lie algebroid, as well as its dual version. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_01735 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Cohomology of Lie algebroids over algebraic spaces Sarkar, Abhishek Differential Geometry K-Theory and Homology We consider Lie algebroids over an algebraic space (or topological ringed space) as quasicoherent sheaves of Lie-Rinehart algebras. We express hypercohomology for a locally free Lie algebroid (not necessarily of finite rank) as a derived functor, and simplify it via Čech cohomology. Furthermore, we define the Hochschild hypercohomology of a sheaf of generalized bialgebras and study the cases of the universal enveloping algebroid and the jet algebroid of a Lie algebroid. In the sequel, we present a version of Hochschild-Kostant-Rosenberg theorem for a locally free Lie algebroid, as well as its dual version. |
| title | Cohomology of Lie algebroids over algebraic spaces |
| topic | Differential Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2111.01735 |