OAI/GroupTheory/PolycyclicRecognition/Algebra/NilpotentQuotientIntegration.lean

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Integrating a nilpotent algebra quotient with a continuous section

Lee's Lie correspondence supplies the integrated homomorphism. Surjectivity, the kernel description, and compact lifts follow from the exponential charts.

  1. theorem OAI.PolycyclicRecognition.exists_surjective_integration_with_section line 27

    Source documentation

    A surjective Lie algebra homomorphism integrates to a surjective group homomorphism with a continuous section obtained from a linear section in logarithmic coordinates.

    theorem exists_surjective_integration_with_section
        [SimplyConnectedSpace N]
        (integrate : NilpotentLieIntegrationInput (EN := EN) (N := N) (EG := EQ) (G := Q))
    …

    Mentions: OAI.PolycyclicRecognition.NilpotentLieIntegrationInput