Asymptotic behaviour of codimensions of p. i. algebras satisfying Capelli identities

Berele, Allan; Regev, Amitai

doi:10.1090/S0002-9947-08-04500-5

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Asymptotic behaviour of codimensions of p. i. algebras satisfying Capelli identities

Authors: Allan Berele and Amitai Regev
Journal: Trans. Amer. Math. Soc. 360 (2008), 5155-5172
MSC (2000): Primary 16R10
Posted: May 27, 2008
MathSciNet review: 2415069
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Abstract: Let be a p. i. algebra with 1 in characteristic zero, satisfying a Capelli identity. Then the cocharacter sequence is asymptotic to a function of the form $an^g\ell^n$ , where $\ell \in \mathbb{N}$ and $g \in \mathbb{Z}$ .

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Additional Information

Allan Berele
Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614
Email: aberele@condor.depaul.edu

Amitai Regev
Affiliation: Department of Theoretical Mathematics, Weizmann Institute, Rehovot, Israel
Email: amitai.regev@wisdom.weizmann.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04500-5
PII: S 0002-9947(08)04500-5
Keywords: Polynomial identities, cocharacter sequence
Received by editor(s): June 5, 2006
Posted: May 27, 2008
Additional Notes: The work of the first author was supported by both the Faculty Research Council of DePaul University and the National Security Agency, under Grant MDA904-500270. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation herein.
The work of the second author was partially supported by ISF grant 947-04.
Article copyright: © Copyright 2008 American Mathematical Society

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