On Split Regular Hom-Leibniz-Rinehart Algebras  

作　　者：Shuangjian GUO Xiaohui ZHANG Shengxiang WANG 

机构地区：[1]School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guizhou 550025,P.R.China [2]School of Mathematical Sciences,Qufu Normal University,Shandong 273165,P.R.China [3]School of Mathematics and Finance,Chuzhou University,Anhui 239000,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2022年第5期481-498,共18页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 12161013);the Key Project of Guizhou University of Finance and Economics (Grant No. 2022KYZD05)。

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+∑_(γ)I_(γ) with U a subspace of a maximal abelian subalgebra H and any I_(γ), a well described ideal of L, satisfying [I_(γ), I_(δ)] = 0 if [γ]≠[δ].In the sequel, we develop techniques of connections of roots and weights for split Hom-LeibnizRinehart algebras, respectively. Finally, we study the structures of tight split regular Hom-Leibniz-Rinehart algebras.

关 键 词：Hom-Leibniz-Rinehart algebra root space weight space decomposition simple ideal 

分 类 号：O15[理学—数学]