Representation Theory of Finite Groups and Finite-Dimensional Algebras

1. Front Matter

   Pages i-ix

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2. Survey Articles

   1. Clifford-Matrices

      • Bernd Fischer

      Pages 1-16

   2. Research in Representation Theory at Mainz (1984–1990)

      • Bertram Huppert

      Pages 17-36

   3. Computational aspects of representation theory of finite groups

      • K. Lux, H. Pahlings

      Pages 37-64

   4. Der Kenntnisstand in der konstruktiven Galoisschen Theorie

      • B. Heinrich Matzat

      Pages 65-98

   5. Contributions to Modular Representation Theory of Finite Groups

      • Gerhard O. Michler

      Pages 99-140

   6. Recent Advances in the Representation Theory of Finite Dimensional Algebras

      • Claus Michael Ringel

      Pages 141-192

   7. The isomorphism problem for integral group rings of finite groups

      • K. W. Roggenkamp

      Pages 193-220

3. Research Articles

   1. Cohen-Macaulay and Gorenstein Artin algebras

      • Maurice Auslander, Idun Reiten

      Pages 221-245

   2. Classical Invariants and the General Linear Group

      • J. A. Green

      Pages 247-272

   3. Partial characters of π-separable groups

      • I. M. Isaacs

      Pages 273-287

   4. First Cohomology Groups for Classical Lie Algebras

      • Jens C. Jantzen

      Pages 289-315

   5. Endotrivial modules and the Auslander-Reiten quiver

      • Christine Bessenrodt

      Pages 317-326

   6. Tame curve singularities with large conductor

      • Ernst Dieterich

      Pages 327-341

   7. Polynomial representations of finite general linear groups in non-describing characteristic

      • Richard Dipper

      Pages 343-370

   8. On Auslander-Reiten components for wild blocks

      • Karin Erdmann

      Pages 371-387

   9. On Gorenstein Algebras

      • Dieter Happel

      Pages 389-404

   10. Decomposition numbers of finite groups of Lie type in non-defining characteristic

       • Gerhard Hiss

       Pages 405-418

   11. Counting blocks of defect zero

       • Reinhard Knörr

       Pages 419-424

   12. Group-theoretical descriptions of ring-theoretical invariants of group algebras

       • Burkhard Külshammer

       Pages 425-442

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 (Bielefeld), G. Michler (Essen), H. Pahlings (Aachen) and C. M. Ringel (Bielefeld) in order to strengthen the interaction between the different re­ search areas in representation theory. The Deutsche Forschungsgemeinschaft has given many research positions and fellowships for young algebraists enabling them to do research at their own uni­ versities or as visitors at well known research institutions in America, Australia, England and France. The whole project benefitted very much from an extensive exchange programme between German and American scientists sponsored by the Deutsche Forschungsgemeinschaft and by the National Science Foundation of the United States. This volume presents lectures given in a final conference and reports by members of the project. It is divided into two parts. The first part contains seven survey articles describing recent advances in different areas of representation theory. These articles do not only concentrate on the work done by the German research groups, but also inform on major developments of the subject at all. The volume omits those topics already treated in book form. In particular, it does not contain a survey on K.

• Galois group
• algebra
• character theory
• cohomology
• finite group
• lie algebra
• matrices
• representation theory

• Institut für Experimentelle Mathematik, Universität GHS Essen, Essen 12, Germany

  G. O. Michler

• Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany

  C. M. Ringel

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