Klaus Wilhelm Roggenkamp
Klaus Wilhelm Roggenkamp (born December 24, 1940 in Hanover ) is a German mathematician who deals with algebra.
Roggenkamp studied mathematics at the University of Gießen from 1960 to 1964 , where he received his doctorate in 1967 under Hermann Boerner ( representations of finite groups in polynomial domains ). He then worked with Irving Reiner at the University of Illinois at Urbana-Champaign and at the University of Montreal . He was a professor at Bielefeld University for four years and then Professor of Algebra at Stuttgart University .
Among other things, he dealt with the group of units in integer group rings in the context of the isomorphism problem of finite group rings (with Leonard Scott ), representation theory of classical orders and higher-dimensional orders. He was invited speaker at the 1990 International Congress of Mathematicians in Kyoto ( The isomorphism problem for integral group rings of finite groups ). He organized several conferences in Oberwolfach , some with Irving Reiner.
The isomorphism problem for group rings ( Graham Higman , Dissertation Oxford 1940) asks whether the isomorphism of the groups follows from the isomorphism of the group ring of two groups G1 and G2 over a field or the whole numbers (conversely, the isomorphism of the groups follows that of the group rings). Roggenkamp and Scott proved this in 1986 for finite p-groups over the p-adic numbers. The positive solution for this case (assumed by Higman as the worst) came unexpectedly at the time. In 1988 he found with Scott a counterexample to a sharper conjecture by Hans Zassenhaus ( a counterexample to the original conjecture by Higman was also found in 2001 by Martin Hertweck in Stuttgart).
He is a member of the Academy of Charitable Sciences in Erfurt and an honorary doctorate from the University of Constanța in Romania.
Fonts
- with Verena Huber-Dyson : Lattices over Orders (= Lecture Notes in Mathematics . 115 and 142). 2 volumes. Springer, Berlin et al. 1970
- with Irving Reiner : Integral representations (= Lecture Notes in Mathematics. 744). Springer, Berlin et al. 1979, ISBN 3-540-09546-2 .
- Integral representations and structure of finite group rings (= Département de Mathématiques, Université de Montréal. Séminaire de Mathématiques Supérieures. 71). Presses de l'Université de Montréal, Montreal 1980, ISBN 2-7606-0485-3 .
- with Martin J. Taylor : Group rings and class groups (= DMV seminar. 18). Birkhäuser, Basel et al. 1992, ISBN 3-7643-2734-0 .
Web links
Individual evidence
- ↑ Klaus Wilhelm Roggenkamp in the Mathematics Genealogy Project (English)
- ^ Roggenkamp, Scott: Isomorphisms of -adic group rings. In: Annals of Mathematics . Series 2, Volume 126, No. 3, 1987, pp. 593-647, doi : 10.2307 / 1971362 .
- ^ Scott: On a conjecture of Zassenhaus and beyond. In: Leonid A. Bokut ', Yu L. Ershov, Aleksei I. Kostikrin (Eds.): Proceedings of the International Conference on Algebra. Dedicated to the Memory of AI Mal'cev (= Contemporary Mathematics . 131, 1). Volume 1. American Mathematical Society, Provicence RI 1992, ISBN 0-8218-5136-5 , pp. 325-343; see Scott, Commentary on Publications
- ↑ Martin Hertweck: A counterexample to the isomorphism problem for integral group rings. In: Annals of Mathematics. Series 2, Volume 154, No. 1, 2001, pp. 115-138, doi : 10.2307 / 3062112 .
| personal data | |
|---|---|
| SURNAME | Roggenkamp, Klaus Wilhelm |
| BRIEF DESCRIPTION | German mathematician |
| DATE OF BIRTH | December 24, 1940 |
| PLACE OF BIRTH | Hanover |