Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • 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

    • 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