分裂的正则Hom-Leibniz-Rinehart代数

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$\gamma]\neqd]$, 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.

On Split Regular Hom-Leibniz-Rinehart Algebras

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.