On Split Regular Hom-Poisson Color Algebras  

作　　者：Shuangjian GUO 

机构地区：[1]School of Mathematics and Statistics, Guizhou University of Finance and Economics

出　　处：《Journal of Mathematical Research with Applications》2019年第5期495-505,共11页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11761017);the Youth Project for Natural Science Foundation of Guizhou Provincial Department of Education(Grant No.KY[2018]155)

摘　　要：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 +Σα Iα with U a subspace of a maximal abelian subalgebra H and any Iα , a well described ideal of A, satisfying [Iα,Iβ]+ IαIβ= 0 if [α]≠[β]. Under certain conditions, in the case of A being of maximal length, the simplicity of the algebra is characterized.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 +αIα with U a subspace of a maximal abelian subalgebra H and any Iα, a well described ideal of A, satisfying[Iα, Iβ] + IαIβ = 0 if [α]≠[β]. Under certain conditions, in the case of A being of maximal length, the simplicity of the algebra is characterized.

关 键 词：Hom-Lie COLOR ALGEBRA Hom-Poisson COLOR ALGEBRA root structure theory 

分 类 号：O1[理学—数学]