# Groups and Symmetries

## From Finite Groups to Lie Groups

Part of the Universitext book series (UTX)

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Textbook

Part of the Universitext book series (UTX)

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.

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

- DOI https://doi.org/10.1007/978-0-387-78866-1
- Copyright Information Springer-Verlag New York 2010
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics
- Print ISBN 978-0-387-78865-4
- Online ISBN 978-0-387-78866-1
- Buy this book on publisher's site