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 c...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.展开更多
基金Supported by NNSF of China (11801121)NSF of Heilongjiang province(QC2018006)the Fundamental Research Fundation for Universities of Heilongjiang Province(LGYC2018JC002)。
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)
文摘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.
