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nLab > Latest Changes: Lie group

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  1.  
    • 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 ℝ 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

  7. Link to category LieGrp.

    diff, v43, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeApr 8th 2021

    added pointer to:

    diff, v44, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeSep 3rd 2021

    added pointer to:

    diff, v48, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeSep 20th 2021

    added pointer to:

    diff, v51, current

    • CommentRowNumber11.
    • CommentAuthorCorbin
    • CommentTimeSep 24th 2021
    • (edited Sep 24th 2021)

    Rewrite paragraph “Lie’s three theorems”:

    • Reconjugate tenses to respect those who will never do maths again
    • Use clearer grammar with better speakability
    • Deduplicate information available on Lie’s three theorems
    • Remove bluelink to the third theorem, which simply redirects to the page on all three

    diff, v52, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeNov 4th 2021

    added pointer to:

    diff, v53, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeMar 20th 2023

    added publication data to:

    diff, v54, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeMay 13th 2024
    • (edited May 13th 2024)

    added pointer to

    diff, v60, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeJun 25th 2024

    added pointer to:

    diff, v61, current

    • CommentRowNumber16.
    • CommentAuthorJoe Moeller
    • CommentTimeSep 10th 2024

1 to 16 of 16

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