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| 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. \begin{document}$L$\end{document}可以表示成\begin{document}$L = U + \sum\limits_{[\alpha] \in \Lambda/\sim}I_{[\alpha]}$\end{document}, 其中\begin{document}$U$\end{document}是交换(阶化)子代数\begin{document}$H$\end{document}的子空间, 任意\begin{document}$I_{[\alpha]}$\end{document}为\begin{document}$L$\end{document}的理想, 并且满足当\begin{document}$[\alpha]\neq [\beta]$\end{document}时, \begin{document}$[I_{[\alpha]}, I_{[\beta]}] = 0$\end{document}. 在一定条件下，定义\begin{document}$L$\end{document}的最大长度和根可积, 证明\begin{document}$L$\end{document}可分解为单(阶化)理想族的直和. |
| 关键词: 双Hom-李color代数 分裂 根空间 根系 |
| DOI： |
| 分类号:O152.5 |
| 基金项目:Supported by NNSF of China (11801121), NSF of Heilongjiang province (QC2018006) and the Fundamental Research Fundation for Universities of Heilongjiang Province (LGYC2018JC002) |
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| ON SPLIT REGULAR BIHOM-LIE COLOR ALGEBRAS |
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Yan CAO,Ya-ling TAO
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| Abstract: |
| 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 \begin{document}$L$\end{document} is of the form \begin{document}$L = U + \sum\limits_{[\alpha] \in \Lambda/\sim}I_{[\alpha]}$\end{document} with \begin{document}$U$\end{document} a subspace of the abelian (graded) subalgebra \begin{document}$H$\end{document} and any \begin{document}$I_{[\alpha]}$\end{document}, a well described (graded) ideal of \begin{document}$L$\end{document}, satisfying \begin{document}$[I_{[\alpha]}, I_{[\beta]}] = 0$\end{document} if \begin{document}$[\alpha]\neq [\beta]$\end{document}. Under certain conditions, in the case of \begin{document}$L$\end{document} being of maximal length, the simplicity of the algebra is characterized and it is shown that \begin{document}$L$\end{document} is the direct sum of the family of its simple (graded) ideals. |
| Key words: BiHom-Lie color algebra split root space root system |
