On the filtration of a free algebra by its associative lower central series

2011/01/29 by George Kerchev, Kerchev, George
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.RA

paper · pdf · doi:10.48550/arxiv.1101.5741

arxiv created 2013/01/03 · arxiv updated 2013/01/04

Abstract

This paper concerns the associative lower central series ideals M_i of the free algebra A_n on n generators. Namely, we study the successive quotients N_i=M_i/M_i+1, which admit an action of the Lie algebra W_n of vector fields on \Bbb Cⁿ. We bound the degree |λ| of tensor field modules F_λ appearing in the Jordan-Hölder series of each N_i, confirming a recent conjecture of Arbesfeld and Jordan. As an application, we compute these decompositions for small n and i.

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