On Split Regular Hom-Leibniz-Rinehart Algebras
Received:February 21, 2022  Revised:June 26, 2022
Key Words: Hom-Leibniz-Rinehart algebra   root space   weight space   decomposition   simple ideal  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12161013) and the Key Project of Guizhou University of Finance and Economics (Grant No.2022KYZD05).
Author NameAffiliation
Shuangjian GUO School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guizhou 550025, P. R. China 
Xiaohui ZHANG School of Mathematical Sciences, Qufu Normal University, Shandong 273165, P. R. China 
Shengxiang WANG School of Mathematics and Finance, Chuzhou University, Anhui 239000, P. R. China 
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      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.
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