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Mat. Sb., 2015, Volume 206, Number 11, Pages 113–130 (Mi msb8474)  

This article is cited in 13 scientific papers (total in 13 papers)

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

A. V. Grishina, S. V. Pchelintsevb

a Moscow State Pedagogical University
b Financial University under the Government of the Russian Federation, Moscow

Abstract: 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, centre of an algebra, core polynomial, proper polynomial, extended Grassmann algebra.
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English version:
Sbornik: Mathematics, 2015, 206:11, 1610–1627

Bibliographic databases:

UDC: 512.552.4
MSC: Primary 16R10; Secondary 15A75, 16S10
Received: 13.01.2015

Citation: A. V. Grishin, S. V. Pchelintsev, “On centres of relatively free associative algebras with a Lie nilpotency identity”, Mat. Sb., 206:11 (2015), 113–130; Sb. Math., 206:11 (2015), 1610–1627

Citation in format AMSBIB
\by A.~V.~Grishin, S.~V.~Pchelintsev
\paper On centres of relatively free associative algebras with a~Lie nilpotency identity
\jour Mat. Sb.
\yr 2015
\vol 206
\issue 11
\pages 113--130
\jour Sb. Math.
\yr 2015
\vol 206
\issue 11
\pages 1610--1627

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    This publication is cited in the following articles:
    1. A. V. Grishin, S. V. Pchelintsev, “Proper central and core polynomials of relatively free associative algebras with identity of Lie nilpotency of degrees 5 and 6”, Sb. Math., 207:12 (2016), 1674–1692  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. V. Grishin, “On the additive structure and asymptotics of codimensions $c_n$ in the algebra $F^{(5)}$”, J. Math. Sci., 233:5 (2018), 666–674  mathnet  crossref  elib
    3. G. Deryabina, A. Krasilnikov, “Products of commutators in a Lie nilpotent associative algebra”, J. Algebra, 469 (2017), 84–95  crossref  mathscinet  zmath  isi  scopus
    4. I. Z. Monteiro Alves, V. Petrogradsky, “Lie structure of truncated symmetric Poisson algebras”, J. Algebra, 488 (2017), 244–281  crossref  mathscinet  zmath  isi  scopus
    5. G. Deryabina, A. Krasilnikov, “Products of several commutators in a Lie nilpotent associative algebra”, Internat. J. Algebra Comput., 27:8 (2017), 1027–1040  crossref  mathscinet  zmath  isi  scopus
    6. S. V. Pchelintsev, “Identities of metabelian alternative algebras”, Siberian Math. J., 58:4 (2017), 693–710  mathnet  crossref  crossref  isi  elib  elib
    7. E. A. da Costa, A. Krasilnikov, “Relations in universal Lie nilpotent associative algebras of class 4”, Commun. Algebr., 46:3 (2018), 1367–1386  crossref  mathscinet  zmath  isi  scopus
    8. A. V. Grishin, “Asymptotics of the Codimensions $c_n$ in the Algebra $F^{(7)}$”, Math. Notes, 104:1 (2018), 22–28  mathnet  crossref  crossref  isi  elib
    9. S. V. Pchelintsev, “Identities of the model algebra of multiplicity 2”, Siberian Math. J., 59:6 (2018), 1105–1124  mathnet  crossref  crossref  isi  elib
    10. A. V. Grishin, “On the measure of inclusion in relatively free algebras with the identity of Lie nilpotency of degree 3 or 4”, Sb. Math., 210:2 (2019), 234–244  mathnet  crossref  crossref  adsnasa  isi  elib
    11. Deryabina G., Krasilnikov A., “Some Products of Commutators in An Associative Ring”, Int. J. Algebr. Comput., 29:2 (2019), 333–341  crossref  mathscinet  zmath  isi  scopus
    12. S. V. Pchelintsev, “Otnositelno svobodnye assotsiativnye Li nilpotentnye algebry ranga $3$”, Sib. elektron. matem. izv., 16 (2019), 1937–1946  mathnet  crossref
    13. S. V. Pchelintsev, “Additivnyi bazis otnositelno svobodnoi assotsiativnoi algebry s tozhdestvom lievoi nilpotentnosti stepeni $5$ i ego primeneniya”, Sib. matem. zhurn., 61:1 (2020), 175–193  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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