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

DOI:
https://doi.org/10.1090/S0002-9939-00-05523-4

Published electronically:
June 21, 2000

MathSciNet review:
1694862

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Let be an associative algebras over a field of characteristic zero. We prove that the codimensions of are polynomially bounded if and only if any finite dimensional algebra with has an explicit decomposition into suitable subalgebras; we also give a decomposition of the -th cocharacter of into suitable -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:
https://doi.org/10.1090/S0002-9939-00-05523-4

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