proposition 14.69 The de~Sitter algebras are isometry algebras

Rests on

• depends_on equation 14.89 eq:lie-sopq-dim ¶
• depends_on proposition 14.59 The Killing fields of a flat pseudo-Euclidean space ¶
  • depends_on definition 13.139 Killing vector ¶
    • depends_on definition 13.120 Isometry ¶
      • depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶
        • depends_on definition 13.48 Differentiable manifold ¶
        • depends_on definition 13.84 Tensor ¶
    • depends_on equation 13.267 eq:mfd-lie-def ¶
  • depends_on equation 14.86 eq:lie-sopq-gen ¶
  • depends_on proposition 13.140 Killing's equation ¶
    • depends_on definition 13.139 Killing vector ¶ ↺
    • depends_on definition 13.149 Metric compatibility ¶
      • depends_on definition 13.145 Affine connection ¶
        • depends_on definition 13.90 Mixed tensor ¶
        • depends_on definition 13.82 Vector field ¶
      • depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶ ↺
      • depends_on definition 13.146 Parallel transport and autoparallels ¶
        • depends_on definition 13.145 Affine connection ¶ ↺
    • depends_on proposition 13.127 Component formulas ¶
      • depends_on definition 13.89 Contravariant and covariant tensors ¶
        • depends_on definition 13.88 General coordinate transformation ¶
      • depends_on definition 13.90 Mixed tensor ¶ ↺
      • depends_on equation 13.267 eq:mfd-lie-def ¶ ↺
      • proves proof ch:11-manifolds-tensors-curvature@proof-28 ¶
    • depends_on theorem 13.150 Levi-Civita connection and contorsion ¶
      • depends_on definition 13.145 Affine connection ¶ ↺
      • depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶ ↺
      • depends_on definition 13.149 Metric compatibility ¶ ↺
      • depends_on definition 13.147 Torsion ¶
        • depends_on definition 13.145 Affine connection ¶ ↺
      • proves proof ch:11-manifolds-tensors-curvature@proof-41 ¶
    • depends_on theorem 13.152 Riemann tensor; Ricci identity with torsion ¶
      • depends_on definition 13.145 Affine connection ¶ ↺
      • depends_on definition 13.147 Torsion ¶ ↺
      • depends_on proposition 7.105 Clairaut–Schwarz ¶
        • depends_on definition 7.20 Continuity at a point ¶
        • depends_on theorem 7.35 Mean value theorem ¶
        • proves proof ch:05-real-analysis@proof-64 ¶
      • proves proof ch:11-manifolds-tensors-curvature@proof-42 ¶
    • proves proof ch:11-manifolds-tensors-curvature@proof-37 ¶
  • proves proof ch:12-lie-groups-fibre-bundles@proof-27 ¶
• depends_on proposition 13.140 Killing's equation ¶ ↺
• proves proof ch:12-lie-groups-fibre-bundles@proof-33 ¶

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