On 3-Hom-Lie-Rinehart algebras

Abstract

We introduce the notion of 3-Hom-Lie-Rinehart algebra and systematically describe a cohomology complex by considering coefficient modules. Furthermore, we consider extensions of a 3-Hom-Lie-Rinehart algebra and characterize the first cohomology space in terms of the group of automorphisms of an A-split abelian extension and the equivalence classes of A-split abelian extensions. Finally, we study formal deformations of 3-Hom-Lie-Rinehart algebras.

Structure and cohomology of 3-Lie-Rinehart superalgebras

“…Related constructions for n-ary hom-Lie algebras and for n-ary hom-Lie superalgebras can be found in [6-9, 17, 29, 41]. The ternary case of (Hom-)Lie Rinehart algebras was developed in [12,13,30].…”