A characterization of algebras with polynomial growth of the codimensions
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- by A. Giambruno and M. Zaicev PDF
- Proc. Amer. Math. Soc. 129 (2001), 59-67 Request permission
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.References
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Additional Information
- A. Giambruno
- Affiliation: Dipartimento di Matematica e Applicazioni, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy
- MR Author ID: 73185
- ORCID: 0000-0002-3422-2539
- Email: a.giambruno@unipa.it
- M. Zaicev
- Affiliation: Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119899 Russia
- MR Author ID: 256798
- Email: zaicev@nw.math.msu.su
- 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
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1694862