Polynomial Detection of Matrix Subalgebras
arXiv:math/0405102
Abstract
It was proved by Giambruno-Sehgal and Chang that the double Capelli polynomial of total degree 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.
6 pages, accepted in the Proceedings of the American Mathematical Society