Work

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

Year: 2026

Type: article

Abstract: 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 $X$ are constructed.

Source: JoNAS - Journal of Non-Associative Structures

DOI: 10.46298/jonas.18002

Authors: Hani Abdelwahab, Ivan Kaygorodov, Bauyrzhan Sartayev

Institution: Mansoura University

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Russian Science Foundation, Fundação para a Ciência e a Tecnologia