Discrete, Finite and Lie Groups : : Comprehensive Group Theory in Geometry and Analysis / / Pietro Giuseppe Fré.

• Superior document: Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2023 English
• VerfasserIn: Fré, Pietro Giuseppe,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2023]; ©2023
• Year of Publication: 2023
• Language: English
• Series: De Gruyter STEM
• Physical Description: 1 online resource (XXII, 508 p.)
• Other title: Frontmatter --; 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783111201535; 9783111319292; 9783111318912; 9783111319230; 9783111318660
• DOI: 10.1515/9783111201535
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Pietro Giuseppe Fré.

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.