A Course in Finite Group Representation Theory

Inbunden, Engelska, 2016

Del i serien Cambridge Studies in Advanced Mathematics

902 kr

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Beskrivning

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Produktinformation

Utgivningsdatum:2016-08-19
Mått:158 x 235 x 23 mm
Vikt:620 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Studies in Advanced Mathematics
Antal sidor:336
Förlag:Cambridge University Press
ISBN:9781107162396

Utforska kategorier

Algebra inom Naturvetenskap och teknik

Mer om författaren

Peter Webb is Professor of Mathematics at the University of Minnesota. His research interests focus on the interactions between group theory and other areas of algebra, combinatorics, and topology. In 1988, he was awarded a Whitehead Prize of the London Mathematical Society.

Recensioner i media

'This is a well-written and motivated book, with carefully chosen topics, examples and exercises to engage the reader, making it suitable in the classroom or for self-study.' Felipe Zaldivar, MAA Reviews

Innehållsförteckning

1. Representations and Maschke's theorem; 2. Algebras with semisimple modules; 3. Characters; 4. Construction of characters; 5. Theorems of Mackey and Clifford; 6. p-groups and the radical; 7. Projective modules for algebras; 8. Projective modules for group algebras; 9. Splitting fields and the decomposition map; 10. Brauer characters; 11. Indecomposable modules; 12. Blocks.