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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 $S$ is very rigid: every ’abstract’ isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is automatically a homeomorphism, provided that $S$ is absolutely simple. If $S$ 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 $\mathbb{R}^n$ 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

• 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

• 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.

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeApr 8th 2021

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeSep 3rd 2021

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeSep 20th 2021

• 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
• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeNov 4th 2021