OAI/GroupTheory/PolycyclicRecognition/Geometry/AlgebraHomLieDifferential.lean

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The actual differential of an algebra-unit homomorphism

Left-invariant vector fields are related to left multiplication in the algebra. Preservation of their brackets gives the matrix commutator law.

  1. def OAI.PolycyclicRecognition.unitsHomDifferential line 24
  2. theorem OAI.PolycyclicRecognition.mfderiv_unitsHom_invariant line 27
  3. theorem OAI.PolycyclicRecognition.lieBracket_rightMultiplication line 58
  4. theorem OAI.PolycyclicRecognition.unitsHomDifferential_map_bracket line 70
  5. def OAI.PolycyclicRecognition.unitsHomLieDifferential line 91
  6. theorem OAI.PolycyclicRecognition.hasMFDerivAt_unitsHomLieDifferential line 100