Skip to Main Content

Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Polynomial detection of matrix subalgebras
HTML articles powered by AMS MathViewer

by Daniel Birmajer PDF
Proc. Amer. Math. Soc. 133 (2005), 1007-1012 Request permission

Abstract:

The double Capelli polynomial of total degree $2t$ is \begin{equation*} \sum \left \{ (\mathrm {sg} \sigma \tau ) x_{\sigma (1)}y_{\tau (1)}x_{\sigma (2)}y_{\tau (2)}\cdots x_{\sigma (t)}y_{\tau (t)} |\; \sigma , \tau \in S_t\right \}. \end{equation*} It was proved by Giambruno-Sehgal and Chang that the double Capelli polynomial of total degree $4n$ is a polynomial identity for $M_n(F)$. (Here, $F$ is a field and $M_n(F)$ is the algebra of $n \times n$ matrices over $F$.) Using a strengthened version of this result obtained by Domokos, we show that the double Capelli polynomial of total degree $4n-2$ is a polynomial identity for any proper $F$-subalgebra of $M_n(F)$. Subsequently, we present a similar result for nonsplit inequivalent extensions of full matrix algebras.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 15A24, 15A99, 16R99
  • Retrieve articles in all journals with MSC (2000): 15A24, 15A99, 16R99
Additional Information
  • Daniel Birmajer
  • Affiliation: Department of Mathematics and Computer Science, Nazareth College, 4245 East Avenue, Rochester, New York 14618
  • Email: abirmaj6@naz.edu
  • Received by editor(s): November 13, 2003
  • Received by editor(s) in revised form: December 22, 2003
  • Published electronically: October 18, 2004
  • Communicated by: Martin Lorenz
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 1007-1012
  • MSC (2000): Primary 15A24, 15A99, 16R99
  • DOI: https://doi.org/10.1090/S0002-9939-04-07631-2
  • MathSciNet review: 2117201