On Split Regular Hom-Leibniz-Rinehart Algebras
On Split Regular Hom-Leibniz-Rinehart Algebras作者机构：School of Mathematical Sciences Qufu Normal University School of Mathematics and Finance Chuzhou University School of Mathematics and Statistics Guizhou University of Finance and Economics
出 版 物：《Journal of Mathematical Research with Applications》 (数学研究及应用(英文版))
年 卷 期：2022年第42卷第5期
页 面：481-498页
核心收录：
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)
主 题：Hom-Leibniz-Rinehart algebra root space weight space decomposition simple ideal
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+∑Iwith U a subspace of a maximal abelian subalgebra H and any I, a well described ideal of L, satisfying [I, I] = 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.
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