Representation Theory of Finite Groups and Finite-Dimensional Algebras
From April 1, 1984 until March 31, 1991 the Deutsche Forschungsgemeinschaft has sponsored the project "Representation Theory of Finite Groups and Finite Di mensional Algebras". The proposal for this project was submitted by B. Huppert (Mainz), B. Fischer
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Series Editors
J. Oesterle A. Weinstein
Representation Theory of Finite Groups and Finite-Dimensional Algebras Proceedings of the Conference at the University of Bielefeld from May 15-17,1991, and 7 Survey Articles on Topics of Representation Theory Edited by G. o. Michler C.M. Ringel
Springer Basel AG
Editor's addresses: Prof. Dr. G. O. Michler Institut flir Experimentelle Mathematik Universitiit GHS Essen Ellernstrasse 29 0-4300 Essen 12
Prof. Dr. C. M. Ringel Universitiit Bielefeld Fakultiit flir Mathematik Universitiitsstrasse 0-4800 Bielefeld
library of Congress Cataloging-in-Pubtication Data Representation tbeory of finite groups and finite-dimensional algebras / edited by G. O. Michler, C. M. Ringel. p. em. - (Progress in mathematics ; v. 95) Includes bibliographical references and index. ISBN 978-3-0348-9720-4 ISBN 978-3-0348-8658-1 (eBook) DOI 10.1007/978-3-0348-8658-1
1. Finite groups. 2. Representations of groups. 3. Representations of algebras. I. Michler, G. (Gerhard), 1938II. Ringel, Claus Michael. III. Title: Finite-dimensional algebras. IV. Series: Progress in mathematics (Boston, Mass.) vol. 95 QA171.R429 1991 512'.2 - dc20
Deutsche Bibtiothek Cataloging-in-Pobtication Data Representation tbeory of finite groups and finite-dimensional algebras / ed. by G. O. Michler; C. M. Ringel. - Basel Boston ; Berlin : Birkhiiuser, 1991 (Progress in mathematics ; Vol. 95) ISBN 978-3-0348-9720-4
NE: Michler, Gerhard O. [Hrsg.]; GT
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use a fee is payable to »Verwertungsgesellschaft Wort«, Munich. © 1991 Springer Basel AG Originally published by Birkhluser Verlag Basel in 1991 Softcover reprint of the hardcover 1st edition 1991 ISBN 978-3-0348-9720-4
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CONTENTS
vii
Preface Contributors
Vlll
1. Survey Articles:
B. Fischer
Clifford-Matrices
B. Huppert
Research in Representation Theory at Mainz (1984-1990)
17
K. Lux, H. Pahlings
Computational Aspects of Representation Theory
37
B.H. Matzat
Der Kenntnisstand in der konstruktiven Galoisschen Theorie
65
G.O. Michler
Contributions to Modular Representation Theory of Finite Groups
99
C.M. Ringel
Recent Advances in the Representation Theory of Finite Dimensional Algebras
141
K.W. Roggenkamp
The isomorphism problem for integral group rings of finite groups
193
M. Auslander, I. Reiten
Cohen-Macaulay and Gorenstein Artin Algebras
221
J .A. Green
Classical Invariants and the General Linear Group
247
M. Isaacs
Partial characters of 7r-separable groups
273
J.C. Jantzen
First Cohomology Groups for Classical Lie Algebras
289
1
2. Research Articles:
vi
C. Bessenrodt
Endotrivial modules and the Auslander-Reiten quiver
317
E. Dieterich
Tame curve singularities with
