On split regular Hom-Leibniz-Rinehart algebras

2020/02/13 by Shuangjian Guo, Xiaohui Zhang, Guo, Shuangjian +3 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2002.06017

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+∑_γI_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-Leibniz-Rinehart algebras respectively. Finally, we study the structures of tight split regular Hom-Leibniz-Rinehart algebras.

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