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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 $c_n$ 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 $[x_1,\dots,x_7]=0$ 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.
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 $c_n$ in the Algebra $F^{(7)}$”, Mat. Zametki, 104:1 (2018), 25–32; Math. Notes, 104:1 (2018), 22–28
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
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