# On split regular BiHom-Poisson superalgebras

## TL;DR

This paper introduces split regular BiHom-Poisson superalgebras, generalizing previous algebraic structures, and develops root connection techniques to analyze their structure and simplicity conditions.

## Contribution

It defines split regular BiHom-Poisson superalgebras and characterizes their structure and simplicity, extending existing algebraic frameworks.

## Key findings

- A decomposition of the algebra into subspaces and ideals.
- Conditions for algebra simplicity in maximal length cases.
- Development of root connection techniques for these algebras.

## Abstract

The paper introduces the class of split regular BiHom-Poisson superalgebras, which is a natural generalization of split regular Hom-Poisson algebras and split regular BiHom-Lie superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular BiHom-Poisson superalgebras $A$ is of the form $A=U+\sum_{\a}I_\a$ with $U$ a subspace of a maximal abelian subalgebra $H$ and any $I_{\a}$, a well described ideal of $A$, satisfying $[I_\a, I_\b]+I_\a I_\b = 0$ if $[\a]\neq [\b]$. Under certain conditions, in the case of $A$ being of maximal length, the simplicity of the algebra is characterized.