Group Representations - 1st Edition - ISBN: 9780444891082, 9781483295107

Group Representations, Volume 4

1st Edition

Authors: Gregory Karpilovsky
eBook ISBN: 9781483295107
Imprint: North Holland
Published Date: 9th March 1995
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Table of Contents

Preface. Part I: Modular Representations. 1. Separable algebras. 2. Cartan invariants, lattices and decomposition numbers. 3. The Brauer - Swan theory. 4. Brauer characters. 5. Quadratic, symplectic and symmetric modules. Part II: Green Theory. 6. Vertices and sources. 7. The Green correspondence. 8. Virtually irreducible lattices. 9. Almost split sequences. 10. The Green ring. Part III: Permutation Modules. 11. An introduction to permutation modules. 12. Hecke algebras. 13. p-Radical groups. 14. p-Permutation modules. 15. Burnside rings. Bibliography. Notation. Index.


This volume is divided into three parts. Part I provides the foundations of the theory of modular representations. Special attention is drawn to the Brauer-Swan theory and the theory of Brauer characters. A detailed investigation of quadratic, symplectic and symmetric modules is also provided. Part II is devoted entirely to the Green theory: vertices and sources, the Green correspondence, the Green ring, etc. In Part III, permutation modules are investigated with an emphasis on the study of p-permutation modules and Burnside rings.

The material is developed with sufficient attention to detail so that it can easily be read by the novice, although its chief appeal will be to specialists. A number of the results presented in this volume have almost certainly never been published before.


© North Holland 1995
North Holland
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About the Authors

Gregory Karpilovsky Author

Affiliations and Expertise

Department of Mathematics, California State University, Chico, CA,