Polynomial Detection of Matrix Subalgebras
Rings and Algebras
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0405102,
title = {Polynomial Detection of Matrix Subalgebras},
author = {Daniel Birmajer},
journal= {arXiv preprint arXiv:math/0405102},
year = {2007}
}
Comments
6 pages, accepted in the Proceedings of the American Mathematical Society