On the lower central series of an associative algebra

Details On the lower central series of an associative algebra On the lower central series of an associative algebra

2007-09-12

arxiv.org/abs/0709.1905v3

Journal of Algebra, Volume 320, Issue 1, 1 July 2008, Pages 213-237

Mathematics

Quantum Algebra

23 pages, latex, corrected some more typos

Scientific paper

10.1016/j.jalgebra.2008.02.019

This paper continues the study of the lower central series quotients of an associative algebra A, regarded as a Lie algebra, which was started in math/0610410 by Feigin and Shoikhet. Namely, it provides a basis for the second quotient in the case when A is the free algebra in n generators (note that the Hilbert series of this quotient was determined earlier in math/0610410). Further, it uses this basis to determine the structure of the second quotient in the case when A is the free algebra modulo the relations saying that the generators have given nilpotency orders. Finally, it determines the structure of the third and fourth quotient in the case of 2 generators, confirming an answer conjectured in math/0610410. Finally, in the appendix, the results of math/0610410 are generalized to the case when A is an arbitrary associative algebra (under certain conditions on $A$).

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