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Polynomial Detection of Matrix Subalgebras

Daniel Birmajer
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Abstract

It was proved by Giambruno-Sehgal and Chang that the double Capelli polynomial of total degree $4n$ is a polynomial identity for the algebra of n by n matrices over a field 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 matrix subalgebra. Subsequently, we present a similar result for nonsplit extensions of full matrix algebras.

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Daniel Birmajer. 2004-05-06. Polynomial Detection of Matrix Subalgebras. https://arxiv.org/abs/math/0405102

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