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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

*-polynomial identities of matrices
with the transpose involution:
The low degrees


Authors: Alain D'Amour and Michel Racine
Journal: Trans. Amer. Math. Soc. 351 (1999), 5089-5106
MSC (1991): Primary 16R10, 16R50
Published electronically: May 21, 1999
MathSciNet review: 1603886
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we investigate $*$-polynomial identities of minimal degree for the algebra of $n\times n$ matrices over a field, where $n<5$ and $*$ is the transpose involution. We first present some basic generators, and then proceed to show that all other minimal degree identities can be derived from those.


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Additional Information

Alain D'Amour
Affiliation: Department of Mathematics & Computer Science, Denison University, Granville, Ohio 43023
Email: damour@cc.denison.edu

Michel Racine
Affiliation: Department of Mathematics, University of Ottawa, Ottawa, Ontario, K1N 6N5, Canada
Email: me@mathstat.uottawa.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02301-6
PII: S 0002-9947(99)02301-6
Received by editor(s): May 18, 1997
Published electronically: May 21, 1999
Additional Notes: The second author’s research is supported in part by a grant from NSERC
Article copyright: © Copyright 1999 American Mathematical Society