Poisson Superalgebras as nonassociative algebras

TL;DR

This paper demonstrates that Poisson superalgebras can be represented as nonassociative algebras with a single multiplication, simplifying their structure and analysis.

Contribution

It introduces a novel approach to view Poisson superalgebras as nonassociative algebras using a unified multiplication operation.

Findings

Poisson superalgebras can be encoded as nonassociative algebras

Simplifies the structural understanding of Poisson superalgebras

Provides a new perspective for algebraic analysis

Abstract

Poisson superalgebras are known as a $\mathbb{Z}_2$-graded vector space with two operations, an associative supercommutative multiplication and a super bracket tied up by the super Leibniz relation. We show that we can consider a single nonassociative multiplication containing all these datas and then consider Poisson superalgebras as non associative algebras.