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Transactions of the American Mathematical Society

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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
Published electronically: May 27, 2008
MathSciNet review: 2415069
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Abstract: Let $A$ be a p. i. algebra with 1 in characteristic zero, satisfying a Capelli identity. Then the cocharacter sequence $c_n(A)$ 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

Amitai Regev
Affiliation: Department of Theoretical Mathematics, Weizmann Institute, Rehovot, Israel

Keywords: Polynomial identities, cocharacter sequence
Received by editor(s): June 5, 2006
Published electronically: 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