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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 5th 2010

    tried to bring the entry Lie group a bit into shape: added plenty of sections and cross links to other nLab material. But there is still much that deserves to be done.

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeOct 6th 2010

    There is the recent preprint

    Linus Kramer, The topology of a simple Lie group is essentially unique, arXiv:1009.5457

    Abstract: We study locally compact group topologies on simple Lie groups. We show that the Lie group topology on such a group SS is very rigid: every ’abstract’ isomorphism between SS and a locally compact and σ\sigma-compact group Γ\Gamma is automatically a homeomorphism, provided that SS is absolutely simple. If SS is complex, then non-continuous field automorphisms of the complex numbers have to be considered, but that is all.

    Not to put pressure on you, Urs. This is as much just a marker for me to put it in later.

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeOct 6th 2010

    Notice that since n\mathbb{R}^n as Lie groups are not simple, this doesn’t apply to the example at Lie group regarding number if Lie group structures.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeOct 6th 2010

    Thanks!

    I have now pasted that into the entry.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 27th 2019

    added this pointer (will also add it at Lie algebra):

    • A. L. Onishchik (ed.) Lie Groups and Lie Algebras

      • I. A. L. Onishchik, E. B. Vinberg, Foundations of Lie Theory,

      • II. V. V. Gorbatsevich, A. L. Onishchik, Lie Transformation Groups

      Encyclopaedia of Mathematical Sciences, Volume 20, Springer 1993

    diff, v40, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 1st 2019
    • (edited Apr 1st 2019)

    Tweaked the sentences under Definition, for better exposition. Much more could be cleaned up in this entry.

    diff, v41, current

  1. Link to category LieGrp.

    diff, v43, current

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