On split regular Hom-Leibniz-Rinehart algebras · arXivDesk
2002.06017Feb 13, 202021pages 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
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+∑γIγ
Nearby in the stack
with
U
a subspace of a maximal abelian subalgebra
H
and any
Iγ
, a well described ideal of
L
, satisfying
[Iγ,Iδ]=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.