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Asymptotics for the multiplicities in the cocharacters of some PI-algebras
Authors:
Francesca Benanti, Antonio Giambruno and Irina Sviridova
Journal:
Proc. Amer. Math. Soc. 132 (2004), 669-679
MSC (2000):
Primary 16R10, 16P90
Posted:
August 13, 2003
MathSciNet review:
2019941
Full-text PDF Free Access
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Abstract: We consider associative PI-algebras over a field of characteristic zero. We study the asymptotic behavior of the sequence of multiplicities of the cocharacters for some significant classes of algebras. We also give a characterization of finitely generated algebras for which this behavior is linear or quadratic.
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- A. Berele and A. Regev, Applications of hook Young diagrams to P.I. algebras, J. Algebra 82 (1983), 559-567. MR 84g:16012
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- A. Berele and A. Regev, On the codimensions of the verbally prime P.I. algebras, Israel J. Math. 91 (1995), 239-247. MR 96g:16028
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- V. S. Drensky and M. Kassabov, Growth of nonmatrix varieties of algebras, preprint.
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- A. Giambruno and M. Zaicev, Minimal varieties of algebras of exponential growth, Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 40-44 (electronic). MR 2001e:16037
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- A. R. Kemer, Ideals of Identities of Associative Algebras, Translations of Math. Monographs 87, Amer. Math. Soc., Providence, RI, 1991. MR 92f:16031
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- D. Krakowski and A. Regev, The polynomial identities of the Grassmann algebra, Trans. Amer. Math. Soc. 181 (1973), 429-438. MR 48:4005
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- V. N. Latyshev, The complexity of nonmatrix varieties of associative algebras. I, II, Algebra i Logika 16 (1977), 149-183, 184-199 (Russian). Translation: Algebra and Logic 16 (1977), 48-122, 122-133. MR 58:27695
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 matrices, J. Algebra 87 (1984), 342-359.MR 86g:16022
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- A. Regev, Existence of identities in
 , Israel J. Math. 11 (1972), 131-152.MR 47:3442
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Additional Information
Francesca Benanti
Affiliation:
Dipartimento di Matematica ed Applicazioni, Università di Palermo, via Archirafi 34, 90123 Palermo, Italy
Email:
fbenanti@math.unipa.it
Antonio Giambruno
Affiliation:
Dipartimento di Matematica ed Applicazioni, Università di Palermo, via Archirafi 34, 90123 Palermo, Italy
Email:
a.giambruno@unipa.it
Irina Sviridova
Affiliation:
Department of Algebra and Geometric Computations, Faculty of Mathematics and Mechanics, Ulyanovsk State University, Ulyanovsk 4327000, Russia
Email:
sviridova_i@rambler.ru
DOI:
http://dx.doi.org/10.1090/S0002-9939-03-07093-X
PII:
S 0002-9939(03)07093-X
Keywords:
Polynomial identities,
multiplicities,
codimensions,
growth
Received by editor(s):
March 22, 2002
Received by editor(s) in revised form:
July 31, 2002, and October 30, 2002
Posted:
August 13, 2003
Additional Notes:
The first and the second authors were partially supported by MURST of Italy
The third author was partially supported by the scientific program “The Universities of Russia"
Communicated by:
Martin Lorenz
Article copyright:
© Copyright 2003 American Mathematical Society
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