On the transposed Poisson n-Lie algebras
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912327929954304 |
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| author | Mashurov, Farukh |
| author_facet | Mashurov, Farukh |
| contents | We study unital commutative associative algebras and their associated n-Lie algebras, showing that they are strong transposed Poisson n-Lie algebras under specific compatibility conditions. Furthermore, we generalize the simplicity criterion for transposed Poisson algebras, proving that a transposed Poisson n-Lie algebra is simple if and only if its associated n-Lie algebra is simple. In addition, we study the strong condition for transposed Poisson n-Lie algebras, proving that it fails in the case of a free transposed Poisson 3-Lie algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01714 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the transposed Poisson n-Lie algebras Mashurov, Farukh Rings and Algebras 17A30, 17A42, 17B63 We study unital commutative associative algebras and their associated n-Lie algebras, showing that they are strong transposed Poisson n-Lie algebras under specific compatibility conditions. Furthermore, we generalize the simplicity criterion for transposed Poisson algebras, proving that a transposed Poisson n-Lie algebra is simple if and only if its associated n-Lie algebra is simple. In addition, we study the strong condition for transposed Poisson n-Lie algebras, proving that it fails in the case of a free transposed Poisson 3-Lie algebra. |
| title | On the transposed Poisson n-Lie algebras |
| topic | Rings and Algebras 17A30, 17A42, 17B63 |
| url | https://arxiv.org/abs/2501.01714 |