Ciro Santilli $$ Sponsor Ciro $$ 中国独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件邓家贵、低端人口、西藏骚乱

Important Lie groups

| 🗖 nosplit | ↑ parent "Lie group" | words: 0 | descendant words: 4k | descendants: 56

🗖 nosplit | ⇓ toc | ↑ parent "Lie group" | words: 0 | descendant words: 4k | descendants: 56

Table of contents | 0, 4k, 56
- 1. Matrix Lie group | 9, 209, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
  - 1.1. Lie algebra of a matrix Lie group | 81 | 🔗 link | 🗖 nosplit | ↑ parent "Matrix Lie group"
  - 1.2. Lie bracket of a matrix Lie group | 119 | 🔗 link | 🗖 nosplit | ↑ parent "Matrix Lie group"
- 2. Classical group | 0, 222, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
  - 2.1. Symplectic group ( $S p (n, F)$ ) | 222, 222, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Classical group"
    - 2.1.1. Symplectic matrix | 🔗 link | 🗖 nosplit | ↑ parent "Symplectic group"
    - 2.1.2. Unitary symplectic group ( $S p (n)$ ) | 🔗 link | 🗖 nosplit | ↑ parent "Symplectic group"
- 3. General linear group ( $G L (n)$ , $G L (n, F)$ ) | 91, 170, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
  - 3.1. Finite general linear group ( $G L (n, F_{m})$ , $G L (n, m)$ ) | 79 | 🔗 link | 🗖 nosplit | ↑ parent "General linear group"
- 4. Special linear group ( $S L (n)$ ) | 18, 638, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
- 5. Orthogonal group ( $O (n)$ ) | 0, 999, 19 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
- 6. Projective linear group | 19, 48, 5 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
  - 6.1. Finite projective linear group ( $P G L (q, p)$ ) | 🔗 link | 🗖 nosplit | ↑ parent "Projective linear group"
  - 6.2. Projective special linear group | 0, 29, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Projective linear group"
    - 6.2.1. Finite projective special linear group ( $P S L (p, q)$ ) | 0, 29, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Projective special linear group"
      - 6.2.1.1. $P S L (2, p)$ | 0, 29, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Finite projective special linear group"
        
        6.2.1.1.1. PSL(2,7) | 29 | 🔗 link | 🗖 nosplit | ↑ parent " $P S L (2, p)$ "
- 7. Poincaré group | 192, 2k, 15 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
  - 7.1. Galilean transformation | 0, 610, 5 | 🔗 link | 🗖 nosplit | ↑ parent "Poincaré group"
    - 7.1.1. Translation (geometry) | 13, 238, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Galilean transformation"
      - 7.1.1.1. Translation group | 19, 225, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Translation"
        
        7.1.1.1.1. The derivative is the generator of the translation group | 206 | 🔗 link | 🗖 nosplit | ↑ parent "Translation group"
    - 7.1.2. Galilean invariance | 285, 372, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Galilean transformation"
      - 7.1.2.1. Covariance | 87 | 🔗 link | 🗖 nosplit | ↑ parent "Galilean invariance"
  - 7.2. Lorentz group ( $S O (1, 3)$ ) | 189, 772, 8 | 🔗 link | 🗖 nosplit | ↑ parent "Poincaré group"

Ancestors

Lie group | 278, 6k, 82
Differential geometry | 12, 6k, 83
Geometry | 0, 8k, 134
Mathematics | 17, 30k, 679
Ciro Santilli's Homepage | 262, 222k, 4k