On the Lower Central Series Quotients of a Graded Associative Algebra
Abstract
We continue the study of the lower central series Li(A) and its successive quotients Bi(A) of a noncommutative associative algebra A, defined by L1(A)=A, Li+1(A)=[A,Li(A)], and Bi(A)=Li(A)/Li+1(A). We describe B2(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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