$δ$-Poisson and transposed $δ$-Poisson algebras
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929583746449408 |
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| author | Abdelwahab, Hani Kaygorodov, Ivan Sartayev, Bauyrzhan |
| author_facet | Abdelwahab, Hani Kaygorodov, Ivan Sartayev, Bauyrzhan |
| contents | We present a comprehensive study of two new Poisson-type algebras. Namely, we are working with $δ$-Poisson and transposed $δ$-Poisson algebras. Our research shows that these algebras are related to many interesting identities. In particular, they are related to shift associative algebras, $F$-manifold algebras, algebras of Jordan brackets, etc. We classify simple $δ$-Poisson and transposed $δ$-Poisson algebras and found their depolarizations. We study $δ$-Poisson and mixed-Poisson algebras to be Koszul and self-dual. Bases of the free $δ$-Poisson and mixed-Poisson algebras generated by a countable set $X$ were constructed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_05490 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $δ$-Poisson and transposed $δ$-Poisson algebras Abdelwahab, Hani Kaygorodov, Ivan Sartayev, Bauyrzhan Rings and Algebras We present a comprehensive study of two new Poisson-type algebras. Namely, we are working with $δ$-Poisson and transposed $δ$-Poisson algebras. Our research shows that these algebras are related to many interesting identities. In particular, they are related to shift associative algebras, $F$-manifold algebras, algebras of Jordan brackets, etc. We classify simple $δ$-Poisson and transposed $δ$-Poisson algebras and found their depolarizations. We study $δ$-Poisson and mixed-Poisson algebras to be Koszul and self-dual. Bases of the free $δ$-Poisson and mixed-Poisson algebras generated by a countable set $X$ were constructed. |
| title | $δ$-Poisson and transposed $δ$-Poisson algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2411.05490 |