On split regular BiHom-Poisson superalgebras
Volume 160 / 2020
Colloquium Mathematicum 160 (2020), 269-282
MSC: Primary 17A60, 17B22; Secondary 17B63.
DOI: 10.4064/cm7809-3-2019
Published online: 17 February 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 $A$.
