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.

16 pages. arXiv admin note: substantial text overlap with arXiv:1808.01909 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