## On split regular BiHom-Poisson superalgebras

### Volume 160 / 2020

#### Abstract

We introduce 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 every split regular BiHom-Poisson superalgebra $A$ is of the form $A=U+\sum _{\alpha }I_\alpha $ where $U$ is a subspace of a maximal abelian subalgebra $H$ and each $I_{\alpha }$ is a well defined ideal of $A$, satisfying $[I_\alpha , I_\beta ]+I_\alpha I_\beta = 0$ if $\alpha \neq \beta $. Under certain conditions, in the case of $A$ of maximal length, we characterize the simplicity of $A$.