Table of contents | 0, 1k, 27
- 1. Important discrete mathematical groups | 0, 11, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Important mathematical groups"
- 2. Lie group | 217, 1k, 21 | 🔗 link | 🗖 nosplit | ↑ parent "Important mathematical groups"
  - 2.1. Applications of Lie groups to differential equations | 102 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"
  - 2.2. Lie algebra | 0, 7, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"
    - 2.2.1. Generator of a Lie algebra | 7 | 🔗 link | 🗖 nosplit | ↑ parent "Lie algebra"
  - 2.3. Continuous symmetry | 18, 308, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"
    - 2.3.1. Local symmetry | 152, 290, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Continuous symmetry"
      - 2.3.1.1. Local symmetries of the Lagrangian imply conserved currents | 138 | 🔗 link | 🗖 nosplit | ↑ parent "Local symmetry"
  - 2.4. Important Lie groups | 0, 693, 13 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"
    - 2.4.1. General linear group ( $G L (n)$ ) | 44 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
    - 2.4.2. Special linear group ( $S L (n)$ ) | 18 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
    - 2.4.3. Orthogonal group ( $O (n)$ ) | 159, 181, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
      - 2.4.3.1. Special orthogonal group ( $S O (n)$ ) | 22 | 🔗 link | 🗖 nosplit | ↑ parent "Orthogonal group"
    - 2.4.4. Unitary group ( $U (n)$ ) | 82, 155, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
      - 2.4.4.1. Unitary group of dimension 2 ( $U (2)$ ) | 5 | 🔗 link | 🗖 nosplit | ↑ parent "Unitary group"
      - 2.4.4.2. Unit circle | 19 | 🔗 link | 🗖 nosplit | ↑ parent "Unitary group"
      - 2.4.4.3. Special unitary group ( $S U (n)$ ) | 49 | 🔗 link | 🗖 nosplit | ↑ parent "Unitary group"
    - 2.4.5. Poincare group | 192, 295, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
      - 2.4.5.1. Galilean transformation | 🔗 link | 🗖 nosplit | ↑ parent "Poincare group"
      - 2.4.5.2. Lorentz group ( $S O (1, 3)$ ) | 61, 103, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Poincare group"
        
        2.4.5.2.1. Lorentz boost | 24 | 🔗 link | 🗖 nosplit | ↑ parent "Lorentz group"
        
        2.4.5.2.2. Indefinite orthogonal group ( $S O (m, n)$ ) | 18 | 🔗 link | 🗖 nosplit | ↑ parent "Lorentz group"
  - 2.5. Representation theory | 61 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"

Ancestors

Group | 0, 3k, 50
Algebra | 0, 3k, 73
Mathematics | 17, 10k, 260
Ciro Santilli's Homepage | 238, 154k, 2k

Important mathematical groups

Ancestors