On the lower central series quotients of a graded associative algebra

TY - JOUR

T1 - On the lower central series quotients of a graded associative algebra

AU - Balagovic, Martina

AU - Balasubramanian, Anirudha

PY - 2011/2/15

Y1 - 2011/2/15

N2 - 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.

AB - 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.

KW - Lower central series;

KW - Kähler differentials;

KW - Noncommutative associative algebra;

UR - http://www.scopus.com/inward/record.url?scp=78650026901&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2010.08.023

DO - 10.1016/j.jalgebra.2010.08.023

M3 - Article

SN - 0021-8693

VL - 328

SP - 287

EP - 300

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -