On split regular Hom-Leibniz-Rinehart algebras

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 $[\gamma ]\ne [\delta ]$. 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.

21pages Welcome any comments. arXiv admin note: substantial text overlap with arXiv:1904.11821, arXiv:1903.12474, arXiv:1902.06260; text overlap with arXiv:1504.04236, arXiv:1706.07084 by other authors

References in corpus (4)

• Hom-algebras and homology
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• 3-Lie-Rinehart Algebras
• On the structure of split regular Hom-Lie Rinehart algebras

Cited by in corpus (1)

• Extensions and crossed modules of $n$-Lie Rinehart algebras