New results on the lower central series quotients of a free associative algebra

2009/02/27 by Noah Arbesfeld, David Jordan · 1 citation
Mathematics · #math.RA #math.QA #math.RT #msc:16W25

paper · pdf · doi:10.1016/j.jalgebra.2009.12.024

published as Volume 323, Issue 6, 15 March 2010, Pages 1813-1825

arxiv created 2009/02/27 · arxiv updated 2010/04/22

Abstract

We continue the study of the lower central series and its associated graded components for a free associative algebra with n generators, as initiated by B. Feigin and B. Shoikhet. We establish a linear bound on the degree of tensor field modules appearing in the Jordan-Hoelder series of each graded component, which is conjecturally tight. We also bound the leading coefficient of the Hilbert polynomial of each graded component. As applications, we confirm conjectures of P. Etingof and B. Shoikhet concerning the structure of the third graded component.

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• Lower central series of free algebras in symmetric tensor categories

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