| On Split Regular Hom-Poisson Color Algebras |
| Received:December 20, 2018 Revised:March 03, 2019 |
| Key Words:
Hom-Lie color algebra Hom-Poisson color algebra root structure theory
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| Fund Project: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). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2019.05.006 |
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