Hom 3-Lie-Rinehart Algebras

Abstract

After endowing with a 3-Lie-Rinehart structure on Hom 3-Lie algebras, we obtain a class of special Hom 3-Lie algebras, which have close relationships with representations of commutative associative algebras. We provide a special class of Hom 3-Lie-Rinehart algebras, called split regular Hom 3-Lie-Rinehart algebras, and we then characterize their structures by means of root systems and weight systems associated to a splitting Cartan subalgebra.

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].…”