On Split Regular Hom-Poisson Color Algebras
Received:December 20, 2018  Revised:March 03, 2019
Key Word: Hom-Lie color algebra   Hom-Poisson color algebra   root   structure theory
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11761017) and the Youth Project for Natural Science Foundation of Guizhou Provincial Department of Education (Grant No.KY[2018]155).
 Author Name Affiliation Shuangjian GUO School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guizhou 550025, P. R. China
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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.