$δ$-Poisson and transposed $δ$-Poisson algebras

Fuente: arXiv
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Main Authors: Abdelwahab, Hani, Kaygorodov, Ivan, Sartayev, Bauyrzhan
Format: Preprint
Published: 2024
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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
id 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