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