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A characterization of algebras with polynomial growth of the codimensions
Author(s):
A.
Giambruno;
M.
Zaicev
Journal:
Proc. Amer. Math. Soc.
129
(2001),
59-67.
MSC (1991):
Primary 16R10, 16R50;
Secondary 16P99
Posted:
June 21, 2000
MathSciNet review:
1694862
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Abstract:
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:
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
Posted:
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
Copyright of article:
Copyright
2000,
American Mathematical Society
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