Group Theory Summary Cheatsheet

A compact, 5-column landscape-format summary of key topics in group theory, Lie groups, and representation theory.

Contents

• Group axioms, types of groups, and examples
• Group actions, orbits, and stabilizers
• Subgroups, normal subgroups, conjugacy classes
• Group homomorphisms and isomorphism theorems
• Group representations and regular representations
• Irreducibility, Schur’s Lemma, and character theory
• Character tables and orthogonality relations
• Symmetric and cyclic group examples
• Lie groups and Lie algebras: definitions and examples
• Exponential maps, adjoint representations, and BCH formula
• SU(2), SO(3), SL(2, ℂ) structure and representation theory
• Tensor products and Clebsch-Gordan decomposition
• Jordan normal form, spectral theorem, and matrix tools
• Summary of key isomorphisms and exponential surjectivity
• Important series expansions and physics notations

Usage

• Compile cheatsheet.tex with pdflatex
• Designed for A4 landscape printing (5 columns)