关于可裂正则BiHom-Poisson超代数
On split regular BiHom-Poisson superalgebras
摘要：
引入了可裂正则BiHom-Poisson超代数类，它是可裂正则Hom-Poisson代数和可裂正则BiHom-Lie超代数的自然推广.通过发展这类代数的根联络技巧，我们证明了这样一个分裂正则BiHom-Poisson超代数$A$是$A=U+\sum_{\a}I_\a$的形式，其中$U$是极大交换子代数$H$的子空间，且$A$的理想$I_{\a}$满足$[I_\a, I_\b]+I_\a I_\b = 0$，如果$[\a]\neq [\b]$ .在一定条件下，当$A$具有极大长度时，刻画了该代数的单性.
英文摘要：
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.
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