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Symmetric forms, idempotents and involutary antiisomorphisms

Published online by Cambridge University Press:  22 January 2016

Peter Landrock  and
Olaf Manz
Peter Landrock*
Affiliation:
Department of Mathematics University of Aarhns, DK-8000 Aarhus, Denmark
Olaf Manz*
Affiliation:
Department of Mathematics (IWR) University of Heidelberg, D-6900 Heidelberg, Germany
*
UCI Utility Consultants International, D-6000 Frankfurt 71
UCI Utility Consultants International, D-6000 Frankfurt 71
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Let G be a finite group, F a field and M an irreducible F[G]-module. By ^ we denote the F-linear involutary antiautomorphism of F[G], induced by inversion on group elements. Suppose that char (F) ≠. 2. We then show that M carries a non-singular G-invariant symmetric bilinear form with values in F if and only if there exists a ^-invariant idempotent e ∈ F [G] which generates the projective cover of M. This extends earlier results of W. Willems [Wi]. The assertion is not true if char(F) = 2.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 125 , March 1992 , pp. 33 - 51
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

References

[Al] Albert, A., Structure of algebras, AMS Colloquium Publications, 1939.CrossRefGoogle Scholar
[BM] Blake, I. F., Mullin, R. C., The mathematical theory of coding, Academic Press, New York, 1975.Google Scholar
[CR] Curtis, C., Reiner, I., Methods of representation theory, John Wiley, New York 1981.Google Scholar
[HB] Huppert, B., Blackburn, N., Finite groups II, Springer-Verlag, Berlin, 1982.CrossRefGoogle Scholar
[La] Landrock, P., Finite group algebras and their modules, Cambridge University Press, Cambridge, 1983.CrossRefGoogle Scholar
[OT] Okuyama, T., Tsushima, Y., On a conjecture of P. Landrock, J. Algebra 104 (1986), 203–208.Google Scholar
[Wi] Willems, W., Metrische Moduln über Gruppenringen, Dissertation, Mainz, 1976.Google Scholar