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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

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