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Standard identities for skew-symmetric matrices

✍ Scribed by Jordan Dale Hill

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 137 KB
Volume: 429
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.04.006

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✦ Synopsis

Let n be a positive, even integer and let K n (F ) denote the subspace of skew-symmetric matrices of Mn(F ), the full matrix algebra with coefficients in a field F. A theorem of Kostant states that K n (F) satisfies the (2n -2)-fold standard identity s 2n-2 . In this paper we refine this result by showing that s 2n-2 may be written non-trivially as the sum of two polynomial identities of K n (F).

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