An alternative approach to deformations of restricted Lie-Rinehart algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918086719832064 |
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| author | Ehret, Quentin |
| author_facet | Ehret, Quentin |
| contents | In this paper, we develop a new approach to the deformation theory of restricted Lie-Rinehart algebras in positive characteristic, based on the deformation theory of restricted morphisms introduced in our earlier work. We provide a full cohomology complex adapted to restricted Lie-Rinehart algebras in characteristic 2, define formal deformations, study obstructions and equivalence classes, and show that these are controlled by the cohomology we introduce. In characteristic $p\geq 3$, we construct 2-cocycles and investigate their relationship with formal deformations. Explicit computations are given in characteristic 2 to illustrate the theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14527 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An alternative approach to deformations of restricted Lie-Rinehart algebras Ehret, Quentin Representation Theory 17B50, 17B56, 17B60, 16W25 In this paper, we develop a new approach to the deformation theory of restricted Lie-Rinehart algebras in positive characteristic, based on the deformation theory of restricted morphisms introduced in our earlier work. We provide a full cohomology complex adapted to restricted Lie-Rinehart algebras in characteristic 2, define formal deformations, study obstructions and equivalence classes, and show that these are controlled by the cohomology we introduce. In characteristic $p\geq 3$, we construct 2-cocycles and investigate their relationship with formal deformations. Explicit computations are given in characteristic 2 to illustrate the theory. |
| title | An alternative approach to deformations of restricted Lie-Rinehart algebras |
| topic | Representation Theory 17B50, 17B56, 17B60, 16W25 |
| url | https://arxiv.org/abs/2504.14527 |