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arXiv · 2411.05490

$\delta$-Poisson and transposed $\delta$-Poisson algebras

Hani Abdelwahab·Ivan Kaygorodov·Bauyrzhan Sartayev
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Abstract

We present a comprehensive study of two new Poisson-type algebras. Namely, we are working with $\delta$-Poisson and transposed $\delta$-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 $\delta$-Poisson and transposed $\delta$-Poisson algebras and found their depolarizations. We study $\delta$-Poisson and mixed-Poisson algebras to be Koszul and self-dual. Bases of the free $\delta$-Poisson and mixed-Poisson algebras generated by a countable set $X$ are constructed.

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Hani Abdelwahab, Ivan Kaygorodov, Bauyrzhan Sartayev. 2024-11-08. $\delta$-Poisson and transposed $\delta$-Poisson algebras. https://doi.org/10.46298/jonas.18002

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