On the generalized Poisson and transposed Poisson algebras

TL;DR

This paper characterizes the polynomial identities of algebras that are both generalized Poisson and transposed Poisson, establishing foundational identities and extending Ito's theorem to this class.

Contribution

It introduces a unified approach to defining identities for these algebras and proves that Ito's theorem applies to generalized Poisson algebras.

Findings

Identifies polynomial identities for the combined algebraic structures

Establishes defining identities using a single operation

Proves Ito's theorem for generalized Poisson algebras

Abstract

We provide the polynomial identities of algebras that are both generalized Poisson algebras and transposed Poisson algebras. We establish defining identities via single operation for generalized Poisson algebras and prove that Ito's theorem holds for generalized Poisson algebras.