## Overview

- Connects students to many branches of mathematics (algebra, geometry, and analysis)
- Applies material to chemistry and physics
- Includes abundant exercises, many with hints or complete solutions

Part of the book series: Universitext (UTX)

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## Table of contents (9 chapters)

## Keywords

## About this book

*Groups and Symmetries: From Finite Groups to Lie Groups* presents an introduction to the theory of group representations and its applications in quantum mechanics. Accessible to advanced undergraduates in mathematics and physics as well as beginning graduate students, the text deals with the theory of representations of finite groups, compact groups, linear Lie groups and their Lie algebras, concisely and in one volume. Prerequisites include calculus and linear algebra.

This new edition contains an additional chapter that deals with Clifford algebras, spin groups, and the theory of spinors, as well as new sections entitled “Topics in history” comprising notes on the history of the material treated within each chapter. (Taken together, they constitute an account of the development of the theory of groups from its inception in the 18^{th} century to the mid-20^{th}.)

References for additional resources and further study are provided in each chapter. All chapters end with exercises of varying degree of difficulty, some of which introduce new definitions and results. The text concludes with a collection of problems with complete solutions making it ideal for both course work and independent study.

Key Topics include:

- 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
- Spin groups and spinors

## Reviews

## Authors and Affiliations

## About the author

A former student of the École Normale Supérieure in Paris, **Yvette Kosmann-Schwarzbach** holds a Doctorat d’État in mathematics as well as a degree in physics from the University of Paris. She has been a professor of mathematics at the University of Lille, at Brooklyn College of the City University of New York, and at the École Polytechnique (France). She has organized numerous conferences, and has held visiting positions and lectured on four continents.

*The Noether Theorems*,

*Invariance and Conservation Laws in the Twentieth Century*(Sources and Studies in the History of Mathematics and Physical Sciences), she has published over 90 research articles in differential geometry, algebra and mathematical physics, and has co-edited

*The Verdier Memorial Conference on Integrable Systems*(Progress in Mathematics),

*Integrability of Nonlinear Systems*(Lecture Notes in Physics) and

*Discrete Integrable Systems*(LectureNotes in Physics).

## Bibliographic Information

Book Title: Groups and Symmetries

Book Subtitle: From Finite Groups to Lie Groups

Authors: Yvette Kosmann-Schwarzbach

Translated by: Stephanie Frank Singer

Series Title: Universitext

DOI: https://doi.org/10.1007/978-3-030-94360-8

Publisher: Springer Cham

eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

Copyright Information: Springer Nature Switzerland AG 2022

Softcover ISBN: 978-3-030-94359-2Published: 17 July 2022

eBook ISBN: 978-3-030-94360-8Published: 16 July 2022

Series ISSN: 0172-5939

Series E-ISSN: 2191-6675

Edition Number: 2

Number of Pages: XIX, 251

Number of Illustrations: 29 b/w illustrations

Additional Information: Original French edition published by Éditions de l'École Polytechnique, 2005.

Topics: Algebra, Group Theory and Generalizations, Applications of Mathematics, Theoretical, Mathematical and Computational Physics, Quantum Physics, Crystallography and Scattering Methods