分裂的正则双Hom-李Color代数  

ON SPLIT REGULAR BIHOM-LIE COLOR ALGEBRAS

作　　者：曹燕 陶雅玲[1] CAO Yan;TAO Ya-ling(School of science,Harbin University of Science and Technology,Harbin 150080,China;Heilongjiang Provincial Key Laboratory of Optimization Control and intelligent Analysis for Complex Systems,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学,理学院数学系,黑龙江哈尔滨150080 [2]哈尔滨理工大学,黑龙江省复杂系统优化控制与智能分析重点实验室,黑龙江哈尔滨150080

出　　处：《数学杂志》2022年第1期49-62,共14页Journal of Mathematics

基　　金：Supported by NNSF of China (11801121);NSF of Heilongjiang province(QC2018006);the Fundamental Research Fundation for Universities of Heilongjiang Province(LGYC2018JC002)。

摘　　要：本文研究了任意分裂的正则双Hom-李color代数的结构.利用此种代数的根连通,得到了带有对称根系的分裂的正则双Hom-李color代数.L可以表示成L=U+∑_([α]∈A/~)I_([α])其中U是交换(阶化)子代数H的子空间,任意I[α]为L的理想,并且满足当[α]≠[β]时,[I_([α]),I_([β])]=0.在一定条件下,定义L的最大长度和根可积,证明L可分解为单(阶化)理想族的直和.The aim of this article is to study the structure of split regular BiHom-Lie color algebras.By developing techniques of connections of roots for this kind of algebras,we show that such a split regular BiHom-Lie color algebra L is of the form L=U+∑_([α]∈A/~)I_([α]) with U a subspace of the abelian(graded) subalgebra H and any I[α],a well described(graded) ideal of L,satisfying[I_([α]),I_([β])]=0 if[α]≠[β].Under certain conditions,in the case of L being of maximal length,the simplicity of the algebra is characterized and it is shown that L is the direct sum of the family of its simple(graded) ideals.

关 键 词：双Hom-李color代数 分裂 根空间 根系 

分 类 号：O152.5[理学—数学]