2024/01/27 by Cody Tipton, Tipton, Cody
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2401.15310
openalex publication_date 2024/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the operad n-Lied, whose algebras are graded n-Lie algebras with degree d n-arity operations, which were introduced in Nambu mechanics and later studied in the algebraic setting with Filippov. We compute the Koszul dual of n-Lied, called n-Com-d+n-2, whose relations are derived from the Specht module S(n,n-1) for a partition (n,n-1) of 2n-1. The intrinsic connection between these two operads come from the eigenvalues of the sequence of graphs \On\n≥ 0, called the Odd graphs, whose spectrum is related to the lower triangular sequence \Er,n\, called the Catalan triangle.