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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.10845 |
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| _version_ | 1866910334214733824 |
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| author | Beltita, Daniel Dobrogowska, Alina Jakimowicz, Grzegorz |
| author_facet | Beltita, Daniel Dobrogowska, Alina Jakimowicz, Grzegorz |
| contents | We study Lie-Rinehart algebra structures in the framework provided by a duality pairing of modules over a unital commutative associative algebra. Thus, we construct examples of Lie brackets corresponding to a fixed anchor map whose image is a cyclic submodule of the derivation module, and therefore we call them cyclic Lie-Rinehart algebras. In a very special case of our construction, these brackets turn out to be related to certain differential operators that occur in mathematical physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10845 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cyclic Lie-Rinehart algebras Beltita, Daniel Dobrogowska, Alina Jakimowicz, Grzegorz Differential Geometry Mathematical Physics Rings and Algebras Primary 17B80, Secondary 58H05 We study Lie-Rinehart algebra structures in the framework provided by a duality pairing of modules over a unital commutative associative algebra. Thus, we construct examples of Lie brackets corresponding to a fixed anchor map whose image is a cyclic submodule of the derivation module, and therefore we call them cyclic Lie-Rinehart algebras. In a very special case of our construction, these brackets turn out to be related to certain differential operators that occur in mathematical physics. |
| title | Cyclic Lie-Rinehart algebras |
| topic | Differential Geometry Mathematical Physics Rings and Algebras Primary 17B80, Secondary 58H05 |
| url | https://arxiv.org/abs/2402.10845 |