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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Semi-invariants and weights of group algebras
of finite groups


Authors: D. S. Passman and P. Wauters
Journal: Proc. Amer. Math. Soc. 127 (1999), 1323-1329
MSC (1991): Primary 16S34, 20D15, 20D45
Published electronically: February 4, 1999
MathSciNet review: 1476385
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the semi-invariants and weights of a group algebra $K[G]$ over a field $K$ of characteristic zero. Specifically, we show that certain basic results which hold when $G$ is a polycyclic-by-finite group with $\Delta ^{+}(G) = 1$ need not hold in the case of group algebras of finite groups. This turns out to be a purely group theoretic question about the existence of class preserving automorphisms.


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Additional Information

D. S. Passman
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: passman@math.wisc.edu

P. Wauters
Affiliation: Department of Mathematics, Limburgs Universitair Centrum, B-3590 Diepenbeek, Belgium
Email: pwauters@luc.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04694-8
PII: S 0002-9939(99)04694-8
Received by editor(s): September 2, 1997
Published electronically: February 4, 1999
Additional Notes: The first author’s research was supported in part by NSF Grant DMS-9622566. The second author’s research was supported by an F.W.O.-grant (Belgium). He wishes to thank the Department of Mathematics of the University of Wisconsin-Madison and, in particular, Donald S. Passman and his wife Marjorie for their warm hospitality.
Communicated by: Lance W. Small
Article copyright: © Copyright 1999 American Mathematical Society