engleski

On the Lower Central Series Quotients of a Graded Associative Algebra

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.

Lower central series ; Kähler differentials ; Noncommutative associative algebra

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