Hochschild cohomology of Lie-Rinehart algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914645690810368 |
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| author | Kosmeijer, Bjarne Posthuma, Hessel |
| author_facet | Kosmeijer, Bjarne Posthuma, Hessel |
| contents | We compute the Hochschild cohomology of universal enveloping algebras of Lie-Rinehart algebras in terms of the Poisson cohomology of the associated graded quotient algebras. Central in our approach are two cochain complexes of "nonlinear Chevalley-Eilenberg" cochains whose origins lie in Lie-Rinehart modules "up to homotopy", one on the Hochschild cochains of the base algebra, another related to the adjoint representation. The Poincare-Birkhoff-Witt isomorphism is then extended to a certain intertwiner between such modules. Finally, exploiting the twisted Calabi-Yau structure, we obtain results for the dual Hochschild and cyclic homology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14654 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hochschild cohomology of Lie-Rinehart algebras Kosmeijer, Bjarne Posthuma, Hessel Rings and Algebras K-Theory and Homology 16E40, 53D17 We compute the Hochschild cohomology of universal enveloping algebras of Lie-Rinehart algebras in terms of the Poisson cohomology of the associated graded quotient algebras. Central in our approach are two cochain complexes of "nonlinear Chevalley-Eilenberg" cochains whose origins lie in Lie-Rinehart modules "up to homotopy", one on the Hochschild cochains of the base algebra, another related to the adjoint representation. The Poincare-Birkhoff-Witt isomorphism is then extended to a certain intertwiner between such modules. Finally, exploiting the twisted Calabi-Yau structure, we obtain results for the dual Hochschild and cyclic homology. |
| title | Hochschild cohomology of Lie-Rinehart algebras |
| topic | Rings and Algebras K-Theory and Homology 16E40, 53D17 |
| url | https://arxiv.org/abs/2312.14654 |