On the lower central series quotients of a graded associative algebra

Martina Balagovic, Anirudha Balasubramanian

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)287-300
Number of pages14
JournalJournal of Algebra
Issue number1
Publication statusPublished - 15 Feb 2011


  • Lower central series;
  • Kähler differentials;
  • Noncommutative associative algebra;

Cite this