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Sbornik: Mathematics, 2019, Volume 210, Issue 2, Pages 234–244
DOI: https://doi.org/10.1070/SM9034 (Mi sm9034) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On the measure of inclusion in relatively free algebras with the identity of Lie nilpotency of degree 3 or 4

A. V. Grishin

Moscow State Pedagogical University, Moscow, Russia
English version PDF (480 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM9034
Abstract: This work is concerned with the concept of a graded subspace of the polylinear part of a relatively free algebra and with the measure of inclusion of such a subspace. Other asymptotic characteristics are also considered. In the case of relatively free algebras with the identity of Lie nilpotency of degree 3 and 4, the measure of inclusion is computed for many subspaces; in particular, for the centre and the $T$-space generated by the commutator this measure is $1/2$.
Bibliography: 17 titles.
Keywords: identity of Lie nilpotency, Frobenius relations, graded subspace, measure of inclusion, rate of growth.
Received: 04.11.2017 and 11.04.2018
Russian version:
Matematicheskii Sbornik, 2019, Volume 210, Number 2, Pages 75–86
DOI: https://doi.org/10.4213/sm9034
Bibliographic databases:
Document Type: Article
UDC: 517.538
MSC: Primary 16R10; Secondary 16R40
Language: English
Original paper language: Russian
Citation: 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
Citation in format AMSBIB
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\paper On the measure of inclusion in relatively free algebras with the identity of Lie nilpotency of degree~3 or~4
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\pages 234--244
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:356
    Russian version PDF:28
    English version PDF:11
    References:43
    First page:8
     
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