On centres of relatively free associative algebras with a Lie nilpotency identity

Abstract

We study central polynomials of a relatively free Lie nilpotent algebra of degree . We prove a product theorem, which generalizes the well-known results of Latyshev and Volichenko. We construct generalized Hall polynomials, by using which we prove that the core centre of the algebra is nontrivial for any . We obtain a number of special results when and . Bibliography: 27 titles.