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Matematicheskie Zametki, 2008, Volume 83, Issue 6, Pages 815–824
DOI: https://doi.org/10.4213/mzm3882 (Mi mzm3882) 		 
This article is cited in 7 scientific papers (total in 7 papers)

The Regev Conjecture and Cocharacters for Identities of Associative Algebras of PI-exponent 1 and 2

A. S. Gordienko

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (466 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm3882
Abstract: A result confirming the Regev conjecture for the codimension of associative algebras with unit which are of PI-exponent 2 is obtained. It is proved that the sequence of multiplicities of irreducible summands in proper cocharacters of algebras of PI-exponent 2 is of period 2, beginning with some index, whereas this sequence is constant for the ordinary cocharacters of the algebras of PI-exponent 1.
Keywords: associative algebra, free associative algebra, PI-exponent, algebra of PI-exponent 2, irreducible cocharacter, Young tableau, algebra of polynomial growth.
Received: 11.04.2007
Revised: 25.09.2007
English version:
Mathematical Notes, 2008, Volume 83, Issue 6, Pages 744–752
DOI: https://doi.org/10.1134/S0001434608050209
Bibliographic databases:
UDC: 512.552.4
Language: Russian
Citation: A. S. Gordienko, “The Regev Conjecture and Cocharacters for Identities of Associative Algebras of PI-exponent 1 and 2”, Mat. Zametki, 83:6 (2008), 815–824; Math. Notes, 83:6 (2008), 744–752
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    1. Ioppolo A., “Some Characterizations of Algebras With Involution With Polynomial Growth of Their Codimensions”, Linear Multilinear Algebra, 67:6 (2019), 1217–1230  crossref  mathscinet  zmath  isi  scopus
    2. Koshlukov P., La Mattina D., “Graded Algebras With Polynomial Growth of Their Codimensions”, J. Algebra, 434 (2015), 115–137  crossref  mathscinet  zmath  isi  elib  scopus
    3. A. Giambruno, M. V. Zaicev, “Asymptotic growth of codimensions of identities of associative algebras”, Moscow University Mathematics Bulletin, 69:3 (2014), 125–127  mathnet  crossref  mathscinet
    4. A. S. Gordienko, “Codimensions of generalized polynomial identities”, Sb. Math., 201:2 (2010), 235–251  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. A. S. Gordienko, “A Finiteness Criterion and Asymptotics for Codimensions of Generalized Identities”, Math. Notes, 86:5 (2009), 645–649  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Gordienko A. S., “Regev's conjecture and codimensions of P.I. algebras”, Acta Appl. Math., 108:1 (2009), 33–55  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. S. Gordienko, “Regev's and Amitsur's conjectures for codimensions of generalized polynomial identities”, J. Math. Sci., 164:2 (2010), 188–194  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
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