On split regular Hom-Poisson superalgebras
Received:December 20, 2018  Revised:February 08, 2019
Key Word: Hom-Lie superalgebra, Hom-Poisson superalgebra, root, structure theory.
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 Author Name Affiliation E-mail Shuangjian Guo Guizhou University of Finance and Economics shuangjianguo@126.com
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We introduce the class of split regular Hom-Poisson superalgebras as the natural generalization of split regular Hom-Poisson algebras and the one of split regular Hom-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.