2023/03/20 by Valiollah Khalili, Khalili, Valiollah
Mathematics · #17A60 #17B05 #17B22 #17B60 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #G.0 #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2303.12905
openalex publication_date 2023/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the structure of a graded 3-Lie-Rinehart algebra L over an associative and commutative graded algebra A. For G an abelian group, we show that if (L, A) is a tight G-graded 3-Lie-Rinehart algebra, then L and A decompose as L =\bigoplusi∈ ILi and A =\bigoplusj∈ JAj, where any Li is a non-zero graded ideal of L satisfying [Li1, Li2, Li3]=0 for any i1, i2, i3∈ I different from each other, and any Aj is a non-zero graded ideal of A satisfying Aj Al=0 for any l, j∈ J such that j≠ l, and both decompositions satisfy that for any i∈ I there exists a unique j∈ J such that Aj Li≠ 0. Furthermore, any (Li, Aj) is a graded 3-Lie-Rinehart algebra. Also, under certain conditions, it is shown that the above decompositions of L and A are by means of the family of their, respective, graded simple ideals.