Polynomial Detection of Matrix Subalgebras

Details Polynomial Detection of Matrix Subalgebras Polynomial Detection of Matrix Subalgebras

2004-05-06

arxiv.org/abs/math/0405102v1

Mathematics

Rings and Algebras

6 pages, accepted in the Proceedings of the American Mathematical Society

Scientific paper

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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