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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| Accesso online: | https://arxiv.org/abs/2010.00335 |
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| _version_ | 1866909279996346368 |
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| author | Hassine, A. Ben Chtioui, T. Elhamdadi, M. Mabrouk, S. |
| author_facet | Hassine, A. Ben Chtioui, T. Elhamdadi, M. Mabrouk, S. |
| contents | We introduce a notion of left-symmetric Rinehart algebras, which is a generalization of a left-symmetric algebras. The left multiplication gives rise to a representation of the corresponding sub-adjacent Lie-Rinehart algebra. We construct left-symmetric Rinehart algebra from O-operators on Lie-Rinehart algebra. We extensively investigate representations of a left-symmetric Rinehart algebras. Moreover, we study deformations of left-symmetric Rinehart algebras, which is controlled by the second cohomology class in the deformation cohomology. We also give the relationships between O-operators and Nijenhuis operators on left-symmetric Rinehart algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_00335 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Cohomology and Deformations of left-symmetric Rinehart Algebras Hassine, A. Ben Chtioui, T. Elhamdadi, M. Mabrouk, S. Rings and Algebras Representation Theory Primary 17E05, 53D17, Secondary 14B12, 06B15 We introduce a notion of left-symmetric Rinehart algebras, which is a generalization of a left-symmetric algebras. The left multiplication gives rise to a representation of the corresponding sub-adjacent Lie-Rinehart algebra. We construct left-symmetric Rinehart algebra from O-operators on Lie-Rinehart algebra. We extensively investigate representations of a left-symmetric Rinehart algebras. Moreover, we study deformations of left-symmetric Rinehart algebras, which is controlled by the second cohomology class in the deformation cohomology. We also give the relationships between O-operators and Nijenhuis operators on left-symmetric Rinehart algebras. |
| title | Cohomology and Deformations of left-symmetric Rinehart Algebras |
| topic | Rings and Algebras Representation Theory Primary 17E05, 53D17, Secondary 14B12, 06B15 |
| url | https://arxiv.org/abs/2010.00335 |