分裂的正则Hom-Leibniz-Rinehart代数

On Split Regular Hom-Leibniz-Rinehart Algebras

中文关键词:  Hom-Leibniz-Rinehart代数  根空间  权空间  分解  单理想

英文关键词:Hom-Leibniz-Rinehart algebra  root space  weight space  decomposition  simple ideal

中文摘要:

      作为Hom-Leibniz代数胚的代数类比, 本文引入Hom-Leibniz-Rinehart代数的概念. 证明了分裂的正则Hom-Leibniz-Rinehart代数$L$写成$L=U+\sum_{\gamma}I_\gamma$, 其中$U$为极大交换子代数$H$的子空间和$I_\gamma$为$L$的理想, 若$[\gamma]\neq[d]$, 满足$[I_\gamma, I_d]=0$. 随后分别发展了分裂Hom-Leibniz-Rinehart代数的根和权的连通技术.最后研究了紧致的正则Hom-Leibniz-Rinehart代数的结构.

英文摘要:

      In this paper, we introduce the notion of the Hom-Leibniz-Rinehart algebra as an algebraic analogue of Hom-Leibniz algebroid, and prove that such an arbitrary split regular Hom-Leibniz-Rinehart algebra $L$ is of the form $L=U+\sum_{\gamma}I_\gamma$ with $U$ a subspace of a maximal abelian subalgebra $H$ and any $I_{\gamma}$, a well described ideal of $L$, satisfying $[I_\gamma, I_\delta]= 0$ if $[\gamma]\neq [\delta]$. In the sequel, we develop techniques of connections of roots and weights for split Hom-Leibniz-Rinehart algebras, respectively. Finally, we study the structures of tight split regular Hom-Leibniz-Rinehart algebras.