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

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

2009-02-27

arxiv.org/abs/0902.4899v2

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

Mathematics

Rings and Algebras

Scientific paper

10.1016/j.jalgebra.2009.12.024

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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