On 3-Hom-Lie-Rinehart algebras

Abstract

We introduce the notion of 3-Hom-Lie-Rinehart algebras 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.

Keywords:

• 3-Hom-Lie-Rinehart algebra
• abelian extension
• cohomology
• deformation
• representation

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17A30
• 17B56
• 17B99

Acknowledgments

The authors are grateful to the referee for carefully reading the manuscript and for many valuable comments which largely improved the article.

Additional information

Funding

The paper is supported by the NSF of China (Nos. 12161013 and 11801304), Guizhou Provincial Science and Technology Foundation (No. [2020]1Y005), the Key University Science Research Project of Anhui Province (No. KJ2020A0711) and the Anhui Provincial Natural Science Foundation (No. 1908085MA03).