Version 1 of 1

Table of contents

Initial Aksbel table of contents. · Working · Sep 17, 2026 12:10 · saved by @mujirin

Table of contents

Lie Algebras for Mathematical Physics

From vector spaces and brackets to symmetry, representations, and quantum applications

Read each section in order. Every title can be opened as a TheoryTrace document.

Cover
Copyright
How to read this book
Introduction
Chapter 1: Symmetry, Infinitesimals, and the Idea of a Lie Algebra
Chapter 2: Linear Algebra Foundations
Chapter 3: The Definition of a Lie Algebra
Chapter 4: First Examples and Their Meaning
Chapter 5: The Jacobi Identity and Commutator Geometry
Chapter 6: From Lie Groups to Lie Algebras
Chapter 7: The Exponential Map and the Baker-Campbell-Hausdorff Formula
Chapter 8: Representations and Modules
Chapter 9: The Adjoint Representation, Derivations, and Automorphisms
Chapter 10: Solvable and Nilpotent Lie Algebras
Chapter 11: Semisimple Lie Algebras and the Killing Form
Chapter 12: Cartan Subalgebras and Root Decompositions
Chapter 13: Root Systems, Weyl Groups, and Dynkin Diagrams
Chapter 14: Classification of Complex Semisimple Lie Algebras
Chapter 15: Highest-Weight Theory
Chapter 16: The Universal Enveloping Algebra
Chapter 17: Casimir Operators and Invariant Theory
Chapter 18: Compact Lie Algebras and Unitary Representations
Chapter 19: Real Forms and Noncompact Lie Algebras
Chapter 20: Lie Algebras in Classical Mechanics and Field Theory
Chapter 21: Lie Algebras in Quantum Mechanics
Chapter 22: The Poincare Algebra and Spacetime Symmetry
Chapter 23: Gauge Algebras and the Standard Model
Chapter 24: Advanced Directions and Research-Level Bridges
Conclusion

τ TheoryTrace