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Sbornik: Mathematics, 2010, Volume 201, Issue 2, Pages 235–251
DOI: https://doi.org/10.1070/SM2010v201n02ABEH004071 (Mi sm6386) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Codimensions of generalized polynomial identities

A. S. Gordienko

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (315 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM2010v201n02ABEH004071
Abstract: It is proved that for every finite-dimensional associative algebra $A$ over a field of characteristic zero there are numbers $C\in\mathbb Q_+$ and $t\in\mathbb Z_+$ such that $gc_n(A)\sim Cn^td^n$ as $n\to\infty$, where $d=PI\exp(A)\in\mathbb Z_+$. Thus, Amitsur's and Regev's conjectures hold for the codimensions $gc_n(A)$ of the generalized polynomial identities.
Bibliography: 6 titles.
Keywords: associative algebra, generalized polynomial identity, asymptotic behaviour of codimensions, $PI$-exponent, representation of a symmetric group.
Received: 25.06.2008 and 10.07.2009
Russian version:
Matematicheskii Sbornik, 2010, Volume 201, Number 2, Pages 79–94
DOI: https://doi.org/10.4213/sm6386
Bibliographic databases:
UDC: 512.552.4
MSC: Primary 16R50; Secondary 16R10, 20C30
Language: English
Original paper language: Russian
Citation: A. S. Gordienko, “Codimensions of generalized polynomial identities”, Mat. Sb., 201:2 (2010), 79–94; Sb. Math., 201:2 (2010), 235–251
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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