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Matematicheskie Zametki, 2018, Volume 104, Issue 1, Pages 25–32
DOI: https://doi.org/10.4213/mzm11602 (Mi mzm11602) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Asymptotics of the Codimensions cn in the Algebra F(7)

A. V. Grishin

Moscow State Pedagogical University
Full-text PDF (465 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm11602
Abstract: The paper studies the additive structure of the algebra F(7), i.e., a relatively free associative countably generated algebra with the identity [x1,…,x7]=0 over an infinite field of characteristic ≠2,3. First, the space of proper multilinear polynomials in this algebra is investigated. As an application, estimates for the codimensions cn=dimF(7)n are obtained, where F(7)n stands for the subspace of multilinear polynomials of degree n in the algebra F(7).
Keywords: identity of Lie nilpotency of degree 7, proper polynomial, extended Grassmann algebra, Hall polynomial, inverse polynomial, linking relations.
Received: 23.03.2017
Revised: 11.06.2017
English version:
Mathematical Notes, 2018, Volume 104, Issue 1, Pages 22–28
DOI: https://doi.org/10.1134/S0001434618070039
Bibliographic databases:
Document Type: Article
UDC: 512.552.4
Language: Russian
Citation: A. V. Grishin, “Asymptotics of the Codimensions cn in the Algebra F(7)”, Mat. Zametki, 104:1 (2018), 25–32; Math. Notes, 104:1 (2018), 22–28
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/mzm11602
  • https://doi.org/10.4213/mzm11602
  • https://www.mathnet.ru/eng/mzm/v104/i1/p25
    • This publication is cited in the following 3 articles:
    1. A. V. Grishin, “Asymptotic Behavior in Lie Nilpotent Relatively Free Algebras and Extended Grassmann Algebras”, Math. Notes, 107:6 (2020), 933–938  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. V. Grishin, “The asymptotic approach to the description of the center of a relatively free Lie-nilpotent algebra”, J. Math. Sci., 269:3 (2023), 322–330  mathnet  crossref
    3. 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  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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    Abstract page:382
    Full-text PDF :46
    References:42
    First page:8
     
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