On the Lower Central Series Quotients of a Graded Associative Algebra
Rings and Algebras
2012-07-18 v4
Abstract
We continue the study of the lower central series L_i(A) and its successive quotients B_i(A) of a noncommutative associative algebra A, defined by L_1(A)=A, L_{i+1}(A)=[A,L_i(A)], and B_i(A)=L_i(A)/L_{i+1}(A). We describe B_{2}(A) for A a quotient of the free algebra on two or three generators by the two-sided ideal generated by a generic homogeneous element. We prove that it is isomorphic to a certain quotient of Kaehler differentials on the non-smooth variety associated to the abelianization of A.
Keywords
Cite
@article{arxiv.1004.3735,
title = {On the Lower Central Series Quotients of a Graded Associative Algebra},
author = {Martina Balagovic and Anirudha Balasubramanian},
journal= {arXiv preprint arXiv:1004.3735},
year = {2012}
}
Comments
Some errors in computational data in Appendix A corrected