On the Lower Central Series of Pi-algebras

  title={On the Lower Central Series of Pi-algebras},
  author={Rumen Dangovski and C. Etingof},
In this paper we study the lower central series {Li}i≥1 of algebras with polynomial identities. More specifically, we investigate the properties of the quotients Ni = Mi/Mi+1 of successive ideals generated by the elements Li. We give a complete description of the structure of these quotients for the free metabelian associative algebra A/(A[A,A][A,A]). With methods from Polynomial Identities theory, linear algebra and representation theory we also manage to explain some of the properties of… CONTINUE READING