On the Lower Central Series Quotients of a Graded Associative Algebra

Details On the Lower Central Series Quotients of a Graded Associative Algebra On the Lower Central Series Quotients of a Graded Associative Algebra

2010-04-21

arxiv.org/abs/1004.3735v3

Journal of Algebra, Volume 328, Issue 1, 15 February 2011, Pages 287-300

Mathematics

Rings and Algebras

Scientific paper

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.

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