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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Asymptotic behaviour of codimensions of p. i. algebras satisfying Capelli identities
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by Allan Berele and Amitai Regev PDF
Trans. Amer. Math. Soc. 360 (2008), 5155-5172 Request permission

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
  • Email: aberele@condor.depaul.edu
  • Amitai Regev
  • Affiliation: Department of Theoretical Mathematics, Weizmann Institute, Rehovot, Israel
  • Email: amitai.regev@wisdom.weizmann.ac.il
  • 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.
  • © Copyright 2008 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 5155-5172
  • MSC (2000): Primary 16R10
  • DOI: https://doi.org/10.1090/S0002-9947-08-04500-5
  • MathSciNet review: 2415069