Lie algebra

From Mathematics wiki

Contents 1 Introduction 2 Structure 3 Classification 4 Classical algebras 5 Other physically interesting algebras

Introduction

• Lie groups and generators
• Adjoint representation
• Killing form
• Casimir invariant
  • Quadratic Casimir invariant

Structure

• Cartan subalgebra
• Weight
• Root

Classification

• Racah's theorem

Classical algebras

• su(N)
• su(2)
• su(3)

Other physically interesting algebras

• Lorentz algebra
• Poincaré algebra
• Conformal algebra
• Virasoro algebra