Polynomial detection of matrix subalgebras
Author:
Daniel Birmajer
Journal:
Proc. Amer. Math. Soc. 133 (2005), 10071012
MSC (2000):
Primary 15A24, 15A99, 16R99
Published electronically:
October 18, 2004
MathSciNet review:
2117201
Fulltext PDF Free Access
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Abstract: The double Capelli polynomial of total degree is
It was proved by GiambrunoSehgal and Chang that the double Capelli polynomial of total degree is a polynomial identity for . (Here, is a field and is the algebra of matrices over .) Using a strengthened version of this result obtained by Domokos, we show that the double Capelli polynomial of total degree is a polynomial identity for any proper subalgebra of . Subsequently, we present a similar result for nonsplit inequivalent extensions of full matrix algebras.
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 Qing Chang, Some consequences of the standard polynomial. Proc. Amer. Math. Soc. 104 (1988), no. 3, 707710. MR 0964846 (89i:16014)
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Additional Information
Daniel Birmajer
Affiliation:
Department of Mathematics and Computer Science, Nazareth College, 4245 East Avenue, Rochester, New York 14618
Email:
abirmaj6@naz.edu
DOI:
http://dx.doi.org/10.1090/S0002993904076312
PII:
S 00029939(04)076312
Keywords:
Polynomial identity,
polynomial test,
matrix subalgebra,
double Capelli polynomial
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
Article copyright:
© Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
