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Polynomial detection of matrix subalgebras |
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| Authors: | Daniel Birmajer |
| Affiliation: | Department of Mathematics and Computer Science, Nazareth College, 4245 East Avenue, Rochester, New York 14618 |
| Abstract: | The double Capelli polynomial of total degree  is  It was proved by Giambruno-Sehgal and Chang that the double Capelli polynomial of total degree  is a polynomial identity for  . (Here,  is a field and  is the algebra of  matrices over  .) Using a strengthened version of this result obtained by Domokos, we show that the double Capelli polynomial of total degree  is a polynomial identity for any proper  -subalgebra of  . Subsequently, we present a similar result for nonsplit inequivalent extensions of full matrix algebras. |
| Keywords: | Polynomial identity polynomial test matrix subalgebra double Capelli polynomial |
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