Discrete, Finite and Lie Groups : Comprehensive Group Theory in Geometry and Analysis.

Format:

Book

Author/Creator:

GmbH, Walter de Gruyter.

Series:

De Gruyter STEM Series

Language:

English

Physical Description:

1 online resource (530 pages)

Edition:

1st ed.

Place of Publication:

Berlin/Boston : Walter de Gruyter GmbH, 2023.

Summary:

In a self contained and exhaustive work the author covers Group Theory in its multifaceted aspects, treating its conceptual foundations in a proper logical order. First discrete and finite group theory, that includes the entire chemical-physical field of crystallography is developed self consistently, followed by the structural theory of Lie Algebras with a complete exposition of the roots and Dynkin diagrams lore. A primary on Fibre-Bundles, Connections and Gauge fields, Riemannian Geometry and the theory of Homogeneous Spaces G/H is also included and systematically developed.

Contents:

Intro

Preface

Some remarks about notations

Contents

1 Groups: the intuitive notion

2 Fundamental notions of algebra

3 Groups: noticeable examples and some developments

4 Basic elements of finite group theory

5 Finite subgroups of SO(3): the ADE classification

6 Manifolds and Lie groups

7 The relation between Lie groups and Lie algebras

8 Crystallographic groups and group extensions

9 Monodromy groups of differential equations

10 Structure of Lie algebras

11 Root systems and their classification

12 Lie algebra representation theory

13 Exceptional Lie algebras

14 In depth study of a simple group

15 A primary on the theory of connections and metrics

16 Isometries and the geometry of coset manifolds

17 Functional spaces and non-compact Lie algebras

18 Harmonic analysis and conclusive remarks

A Available MATHEMATICA NoteBooks written by the author

Bibliography

About the author

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783111201535

3111201538

OCLC:

1393306442