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
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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). |
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Abstract: |
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. |
Citation: |
DOI:10.3770/j.issn:2095-2651.2022.05.005 |
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