On Split Regular Hom-Poisson Color Algebras

DOI：10.3770/j.issn:2095-2651.2019.05.006

 作者 单位 郭双建 贵州财经大学数学与统计学院, 贵州 贵阳 550025

作为分裂的正则Hom-Poisson代数和分裂的正则Hom-李着色代数的自然推广, 本文介绍了一类分裂的正则双Hom-Poisson着色代数. 利用这类代数根连通的发展技巧, 本文证明了分裂的正则双Hom-Poisson着色代数$A$写成$A=U+\sum_{\alpha}I_\alpha$, 其中$U$为极大交换子代数$H$的子空间和$I_\alpha$为$A$的理想, 若$[\alpha]\neq[\beta]$, 满足$[I_\a, I_\b]+I_\a I_\b=0$ 在一定条件下, 描述了$A$的最大长度和它的半单性.

We introduce the class of split regular Hom-Poisson color algebras as the natural generalization of split regular Hom-Poisson algebras and the one of split regular Hom-Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Poisson color algebras $A$ 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.