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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
DOI: https://doi.org/10.1090/S0002-9939-03-07093-X
Published electronically: August 13, 2003
MathSciNet review: 2019941
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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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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: https://doi.org/10.1090/S0002-9939-03-07093-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
Published electronically: 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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