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 + γ I γ with U a subspace of a maximal abelian subalgebra H and any I γ , a well described ideal of L, satisfyingIn 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.

Crossed modules for Hom-Leibniz-Rinehart algebras

“…We remark that our definition of Hom-Leibniz-Rinehart algebra is different from [18] since in that paper the conditions (H12), (H21), (H23), (H32) and (H42) are missed so they only consider the special case ρ R L = 0.…”

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

“…In the following definition, we recall the notion of Leibniz Rinehart algebra as a particular case of Hom-Leibniz Rinehart algebra introduced in [26].…”