definition 14.20 Cartan subalgebra and rank

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Supports

• depends_on proposition 14.22 The rank of $\mathfrak{so}(p,q)$ ¶
  • depends_on lemma 14.68 The algebra fixing a timelike momentum ¶
    • depends_on definition A.384 The mass shell and the standard momentum ¶
      • depends_on lemma A.387 Standard boost and transitivity ¶
        • depends_on lemma A.388 The invariant measure ¶
        • depends_on proposition A.390 Construction ¶
      • depends_on lemma A.386 The little group ¶
        • depends_on proposition A.390 Construction ¶ ↺
      • depends_on lemma A.388 The invariant measure ¶ ↺
      • depends_on theorem A.385 Labels of a massive representation ¶
        • depends_on example A.394 $D = 4$ ¶
      • depends_on theorem A.392 Wigner–Mackey classification; quoted ¶
    • depends_on lemma A.386 The little group ¶ ↺
    • depends_on theorem A.385 Labels of a massive representation ¶ ↺
• depends_on proposition 14.50 Dimension and rank ¶
  • depends_on lemma A.378 Real ideals and complex ideals ¶
  • depends_on proposition 14.54 The two Casimir operators of $\mathfrak{su}(3)$ ¶
    • depends_on example A.358 Rank two: $\mathfrak{su}(3)$ ¶
  • depends_on proposition 102.28 The parameters of QCD ¶
  • depends_on theorem A.376 $\mathfrak{su}(3)$ is simple ¶
    • depends_on corollary A.377 The adjoint representation is irreducible ¶
• depends_on theorem A.346 Racah ¶
  • depends_on example A.359 The Lorentz algebra ¶
  • depends_on example A.357 Rank one: $\mathfrak{su}(2)$ ¶
  • depends_on example A.358 Rank two: $\mathfrak{su}(3)$ ¶ ↺
• depends_on theorem A.352 Chevalley's theorem on finite reflection groups, quoted ¶
• depends_on theorem A.351 Chevalley restriction theorem, quoted ¶
• depends_on theorem 14.21 Racah ¶
  • depends_on proposition 14.22 The rank of $\mathfrak{so}(p,q)$ ¶ ↺
  • depends_on proposition 14.54 The two Casimir operators of $\mathfrak{su}(3)$ ¶ ↺
  • depends_on theorem A.385 Labels of a massive representation ¶ ↺