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.
- Group theory is applied in Physics, Chemistry, Crystallography and many further fields.
- Discrete and continuous groups are relevant for probability theory, graph theory, in the theory of games and as well in economical and statistical sciences.
Author(s): Pietro Giuseppe Fré
Series: De Gruyter STEM
Edition: 1
Publisher: De Gruyter
Year: 2023
Language: English
Pages: 508
Tags: Group Theory, Manifolds, Lie Groups, Lie Algebras, Root Systems,Crystallographic Groups, Mondromy Groups, Representation Theory
cover
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
