Geodesic
On centres of relatively free associative algebras with a~Lie nilpotency identity
Sbornik. Mathematics, Tome 206 (2015) no. 11, pp. 1610-1627

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We study central polynomials of a relatively free Lie nilpotent algebra $F^{(n)}$ of degree $n$. 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 $F^{(n)}$ is nontrivial for any $n\geqslant 5$. We obtain a number of special results when $n=5$ and $6$. Bibliography: 27 titles.
Keywords: Lie nilpotency identity, proper polynomial, extended Grassmann algebra.
Mots-clés : centre of an algebra, core polynomial 
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     author = {A. V. Grishin and S. V. Pchelintsev},
     title = {On centres of relatively free associative algebras with {a~Lie} nilpotency identity},
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     number = {11},
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A. V. Grishin; S. V. Pchelintsev. On centres of relatively free associative algebras with a~Lie nilpotency identity. Sbornik. Mathematics, Tome 206 (2015) no. 11, pp. 1610-1627. http://geodesic.mathdoc.fr/item/SM_2015_206_11_a3/