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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.
† Author to whom correspondence should be addressed
DOI:
https://doi.org/10.4213/sm8474
 Full text:
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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
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Linking options:
http://mi.mathnet.ru/eng/msb8474https://doi.org/10.4213/sm8474 http://mi.mathnet.ru/eng/msb/v206/i11/p113
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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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
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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
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G. Deryabina, A. Krasilnikov, “Products of commutators in a Lie nilpotent associative algebra”, J. Algebra, 469 (2017), 84–95
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I. Z. Monteiro Alves, V. Petrogradsky, “Lie structure of truncated symmetric Poisson algebras”, J. Algebra, 488 (2017), 244–281
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G. Deryabina, A. Krasilnikov, “Products of several commutators in a Lie nilpotent associative algebra”, Internat. J. Algebra Comput., 27:8 (2017), 1027–1040
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S. V. Pchelintsev, “Identities of metabelian alternative algebras”, Siberian Math. J., 58:4 (2017), 693–710
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E. A. da Costa, A. Krasilnikov, “Relations in universal Lie nilpotent associative algebras of class 4”, Commun. Algebr., 46:3 (2018), 1367–1386
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A. V. Grishin, “Asymptotics of the Codimensions $c_n$ in the Algebra $F^{(7)}$”, Math. Notes, 104:1 (2018), 22–28
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S. V. Pchelintsev, “Identities of the model algebra of multiplicity 2”, Siberian Math. J., 59:6 (2018), 1105–1124
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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
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Deryabina G., Krasilnikov A., “Some Products of Commutators in An Associative Ring”, Int. J. Algebr. Comput., 29:2 (2019), 333–341
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S. V. Pchelintsev, “Otnositelno svobodnye assotsiativnye Li nilpotentnye algebry ranga $3$”, Sib. elektron. matem. izv., 16 (2019), 1937–1946
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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
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