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Cocharacters, Codimensions and Hilbert Series of the Polynomial Identities for 2 × 2 Matrices with Involution

Published online by Cambridge University Press:  20 November 2018

Vesselin Drensky  and
Antonio Giambruno
Vesselin Drensky
Affiliation:
Institute of Mathematics, Bulgarian Academy of Sciences, Acad. Georgy Bonchev Str. block 8 1113 Sofia Bulgaria
Antonio Giambruno
Affiliation:
Department of Mathematics, University of Palermo, Via Archirafi 34 90123 Palermo, Italy
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Abstract

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Let M2(K, *) be the algebra of 2 × 2 matrices with involution over a field K of characteristic 0. We obtain the exact values of the cocharacters, codimensions and Hilbert series of the *-T-ideal of the polynomial identities for M2(K, *).

Keywords

16R50
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 4 , 01 August 1994 , pp. 718 - 733
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Drensky, V. S., Explicit codimension formulas of certain T-ideals, Sibirsk. Mat. Zh. (6) 29(1988), 30-36 (Russian); English translation: Siberian Math. J. 29(1988), 897-902.Google Scholar
2. Drensky, V., Polynomial identities for 2 × 2 matrices, Acta Appl. Math. 21(1990), 137–161.Google Scholar
3. A. Giambruno, GL × GL-representations and *-polynomial identities, Comm. Algebra 14(1986), 787-796.Google Scholar
4. Giambruno, A. and Regev, A., Wreath products and P.I. algebras, J. Pure Appl. Algebra 35(1985), 133-149.Google Scholar
5. Macdonald, I. G., Symmetric Functions and Hall Polynomials, Oxford Univ. Press, Clarendon, Oxford, 1979.Google Scholar
6. Procesi, C., Computing with 2 × 2 matrices, J. Algebra 87(1984), 342-359.Google Scholar
7. Specht, W., Gesetze in Ringen. I, Math. Z. 52(1950), 557-589.Google Scholar
8. Weyl, H., The Classical Groups, Their Invariants and Representations, Princeton Univ. Press, Princeton, N.J., 1946.Google Scholar