Characters and Automorphism Groups of Compact Riemann Surfaces
Part of London Mathematical Society Lecture Note Series
- Author: Thomas Breuer, Rheinisch-Westfälische Technische Hochschule Aachen
- Date Published: September 2000
- availability: Available
- format: Paperback
- isbn: 9780521798099
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This book deals with automorphism groups of compact Riemann surfaces, of genus at least two, viewed as factor groups of Fuchsian groups. The author uses modern methods from computational group theory and representation theory, providing classifications of all automorphism groups up to genus 48. The book also classifies the ordinary characters for several groups, arising from the action of automorphisms on the space of holomorphic abelian differentials of a compact Reimann surface. This book is suitable for graduate students and researchers in group theory, representation theory, complex analysis and computer algebra.
Read more- Contains an explicit classification of automorphism groups of compact Riemann surfaces
- Uses modern computer algebra tools to solve problems that were posed a hundred years ago
- Covers recent research in the field
Reviews & endorsements
'… by bringing together a number of very effective techniques, and by presenting a mass of specific evidence, Breuer has done the mathematical community a considerable service … the presentation of the material is excellent, with attractive layout … a valuable addition to the literature, which should be essential reading for anyone interested in the connections between Riemann surfaces and finite groups.' G. Jones, Proceedings of the Edinburgh Mathematical Society
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×Product details
- Date Published: September 2000
- format: Paperback
- isbn: 9780521798099
- length: 212 pages
- dimensions: 231 x 313 x 11 mm
- weight: 0.32kg
- contains: 3 b/w illus. 29 tables
- availability: Available
Table of Contents
Preface
Notation
1. Compact Riemann surfaces
2. Group characters
3. Automorphisms of compact Riemann surfaces
4. Generation of groups
5. Classification for small genus
6. Classification for fixed group: real characters
7. Classification for fixed group: nonreal irrationalities
Appendix A. Abelian inariants
Appendix B. Irreducible characters
Appendix C. Maillet's determinant
Bibliography
Index.
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