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 Mat. Zametki, 2018, Volume 104, Issue 1, Pages 25–32 (Mi mz11602)

Asymptotics of the Codimensions $c_n$ in the Algebra $F^{(7)}$

A. V. Grishin

Moscow State Pedagogical University

Abstract: The paper studies the additive structure of the algebra $F^{(7)}$, i.e., a relatively free associative countably generated algebra with the identity $[x_1,…,x_7]=0$ over an infinite field of characteristic $\ne 2,3$. First, the space of proper multilinear polynomials in this algebra is investigated. As an application, estimates for the codimensions $c_n=\dim F_n^{(7)}$ are obtained, where $F_n^{(7)}$ 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.

DOI: https://doi.org/10.4213/mzm11602

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English version:
Mathematical Notes, 2018, 104:1, 22–28

Bibliographic databases:

UDC: 512.552.4
Revised: 11.06.2017

Citation: A. V. Grishin, “Asymptotics of the Codimensions $c_n$ in the Algebra $F^{(7)}$”, Mat. Zametki, 104:1 (2018), 25–32; Math. Notes, 104:1 (2018), 22–28

Citation in format AMSBIB
\Bibitem{Gri18} \by A.~V.~Grishin \paper Asymptotics of the Codimensions~$c_n$ in the Algebra $F^{(7)}$ \jour Mat. Zametki \yr 2018 \vol 104 \issue 1 \pages 25--32 \mathnet{http://mi.mathnet.ru/mz11602} \crossref{https://doi.org/10.4213/mzm11602} \elib{http://elibrary.ru/item.asp?id=35276447} \transl \jour Math. Notes \yr 2018 \vol 104 \issue 1 \pages 22--28 \crossref{https://doi.org/10.1134/S0001434618070039} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000446511500003} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85054379993} 

• http://mi.mathnet.ru/eng/mz11602
• https://doi.org/10.4213/mzm11602
• http://mi.mathnet.ru/eng/mz/v104/i1/p25

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. 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
2. A. V. Grishin, “Asymptotic Behavior in Lie Nilpotent Relatively Free Algebras and Extended Grassmann Algebras”, Math. Notes, 107:6 (2020), 903–908
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