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Groups and Symmetries

From Finite Groups to Lie Groups

  • Yvette Kosmann-Schwarzbach

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Pr Yvette Kosmann-Schwarzbach, Stephanie Frank Singer
    Pages 1-8
  3. Pr Yvette Kosmann-Schwarzbach, Stephanie Frank Singer
    Pages 9-32
  4. Pr Yvette Kosmann-Schwarzbach, Stephanie Frank Singer
    Pages 33-46
  5. Pr Yvette Kosmann-Schwarzbach, Stephanie Frank Singer
    Pages 47-70
  6. Pr Yvette Kosmann-Schwarzbach, Stephanie Frank Singer
    Pages 71-80
  7. Pr Yvette Kosmann-Schwarzbach, Stephanie Frank Singer
    Pages 81-92
  8. Pr Yvette Kosmann-Schwarzbach, Stephanie Frank Singer
    Pages 93-106
  9. Pr Yvette Kosmann-Schwarzbach, Stephanie Frank Singer
    Pages 107-127
  10. Back Matter
    Pages 1-65

About this book

Introduction

Unlike many other texts, this book deals with the theory of representations of finite groups, compact groups, linear Lie groups and their Lie algebras, concisely and in one volume.

Key Topics:

• Brisk review of the basic definitions of group theory, with examples

• Representation theory of finite groups: character theory

• Representations of compact groups using the Haar measure

• Lie algebras and linear Lie groups

• Detailed study of SO(3) and SU(2), and their representations

• Spherical harmonics

• Representations of SU(3), roots and weights, with quark theory as a consequence of the mathematical properties of this symmetry group

This book is illustrated with portraits and a few historical remarks.  With only linear algebra and calculus as prerequisites, Groups and Symmetries: From Finite Groups to Lie Groups is accessible to advanced undergraduates in mathematics and physics, and will still be of interest to beginning graduate students. Exercises for each chapter and a collection of problems with complete solutions make this an ideal text for the classroom and for independent study.

Keywords

Group representation Group theory Lie groups and Lie algrebras Representation theory Symmetry group algebra elementary particles, quarks finite groups linear algebra representations of groups spherical harmonics

Authors and affiliations

  • Yvette Kosmann-Schwarzbach
    • 1
  1. 1.Centre de MathématiquesEcole PolytechniquePalaiseau CedexFrance

Bibliographic information

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