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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A characterization of algebras with polynomial growth of the codimensions


Authors: A. Giambruno and M. Zaicev
Journal: Proc. Amer. Math. Soc. 129 (2001), 59-67
MSC (1991): Primary 16R10, 16R50; Secondary 16P99
Published electronically: June 21, 2000
MathSciNet review: 1694862
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Abstract:

Let $A$ be an associative algebras over a field of characteristic zero. We prove that the codimensions of $A$ are polynomially bounded if and only if any finite dimensional algebra $B$ with $Id(A)=Id(B)$has an explicit decomposition into suitable subalgebras; we also give a decomposition of the $n$-th cocharacter of $A$ into suitable $S_n$-characters.

We give similar characterizations of finite dimensional algebras with involution whose $*$-codimension sequence is polynomially bounded. In this case we exploit the representation theory of the hyperoctahedral group.


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Additional Information

A. Giambruno
Affiliation: Dipartimento di Matematica e Applicazioni, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy
Email: a.giambruno@unipa.it

M. Zaicev
Affiliation: Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899 Russia
Email: zaicev@nw.math.msu.su

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05523-4
PII: S 0002-9939(00)05523-4
Received by editor(s): December 1, 1998
Received by editor(s) in revised form: March 26, 1999
Published electronically: June 21, 2000
Additional Notes: The first author was partially supported by the CNR and MURST of Italy; the second author was partially supported by RFFI, grants 96-01-00146 and 96-15-96050.
Communicated by: Ken Goodearl
Article copyright: © Copyright 2000 American Mathematical Society