2021/03/27 by Abdelkader Ben Hassine, Taoufik Chtioui, Hassine, A. Ben +5
Mathematics · #17E05 #53D17 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2103.15006
openalex publication_date 2021/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a notion of n-Lie Rinehart algebras as a generalization of Lie Rinehart algebras to n-ary case. This notion is also an algebraic analogue of n-Lie algebroids. We develop representation theory and describe a cohomology complex of n-Lie Rinehart algebras. Furthermore, we investigate extension theory of n-Lie Rinehart algebras by means of 2-cocycles. Finally, we introduce crossed modules of n-Lie Rinehart algebras to gain a better understanding of their third dimensional cohomology groups.