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Identities in algebras with involution

Published online by Cambridge University Press:  17 April 2009

Tsetska Grigorova Rashkova
Affiliation:
Centre of Applied Mathematics and InformaticsUniversity of Rousse7017 RousseBulgaria, e-mail: tcetcka@ami.ru.acad.bg
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There is an approach due to Bergman describing ordinary polynomial identities for Mn (K) by means of commutative algebra. In the paper we apply this approach to the matrix algebra of even order M2n (K, *) with symplectic involution *.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Bergman, G.M., ‘Wild automorphisms of free P.I. algebras and some new identities’, (preprint) (1981).Google Scholar
[2]Drensky, V. and Rashkova, T., ‘Weak polynomial identities for the matrix algebra’, Comm. Algebra 21 (1993), 37793795.Google Scholar
[3]Formanek, E., ‘Central polynomials for matrix rings’, J. Algebra 23 (1972), 129132.CrossRefGoogle Scholar
[4]Giambruno, A. and Valenti, A., ‘On minimal *-identities of matrices’, Linear and Multilinear Algebra 39 (1995), 309323.Google Scholar
[5]Rashkova, Ts. and Drensky, V., ‘Identities of representations of Lie algebras and *-polynomial identities’, Rend. Circ. Mat. Palermo 48 (1999), 152163.Google Scholar
[6]Rowen, L.H., Polynomial identities in ring theory (Academic Press, New York, 1980).Google Scholar