definition 14.2 Lie group

Rests on

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Supports

• depends_on definition A.561 Coadjoint action and equivariance ¶
  • depends_on lemma A.567 The differential of the momentum map along the orbit ¶
    • depends_on theorem A.568 The radical is the isotropy orbit ¶
      • depends_on proposition A.570 Existence and uniqueness of the reduced form ¶
        • depends_on proposition A.571 Invariant Hamiltonians descend with their flows ¶
  • depends_on proposition A.566 The isotropy group acts, and the quotient is smooth ¶
    • depends_on proposition A.570 Existence and uniqueness of the reduced form ¶ ↺
  • depends_on theorem A.563 Marsden–Weinstein reduction ¶
    • depends_on example A.573 The abelian case, and eliminating a cyclic coordinate ¶
    • depends_on example A.572 Rotational reduction of the central-force problem ¶
• depends_on definition 24.43 Momentum map ¶
  • depends_on definition A.561 Coadjoint action and equivariance ¶ ↺
  • depends_on example 24.44 Linear and angular momentum ¶
    • depends_on example A.572 Rotational reduction of the central-force problem ¶ ↺
  • depends_on lemma 24.46 The level set of the momentum map is the symplectic orthogonal of the orbit ¶
    • depends_on proposition A.565 Freeness makes every value regular ¶
      • depends_on lemma A.567 The differential of the momentum map along the orbit ¶ ↺
      • depends_on proposition A.566 The isotropy group acts, and the quotient is smooth ¶ ↺
    • depends_on theorem A.563 Marsden–Weinstein reduction ¶ ↺
    • depends_on theorem A.568 The radical is the isotropy orbit ¶ ↺
    • depends_on theorem 24.47 Marsden–Weinstein reduction ¶
      • depends_on remark 24.48 Reduction is what physicists do without saying so ¶
        • depends_on example A.573 The abelian case, and eliminating a cyclic coordinate ¶ ↺
  • depends_on theorem 24.45 Noether, symplectic form ¶
    • depends_on proposition A.571 Invariant Hamiltonians descend with their flows ¶ ↺
• depends_on proposition 14.3 A one-parameter subgroup is an exponential ¶