Not signed in (Sign In)

Start a new discussion

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 bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics 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 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 homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory kan 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 natural nforum nlab nonassociative 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 string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topological topology topos topos-theory 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 21st 2020

    added

    • more hyperlinks (and some whitespace) to the paragraph on maximal tori.

    • the statement that smooth actions of compact Lie groups on smooth manifolds are proper

    diff, v9, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeOct 23rd 2020

    Corrected the reference: it’s Corollary 21.6 in the actual second edition.

    diff, v10, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 24th 2020

    Ah, thanks.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMar 13th 2021

    added a section “Applications – In equivariant homotopy theory” (here) with this remark:

    Compact Lie groups make a somewhat unexpected appearance as equivariance groups in equivariant homotopy theory, where the compact Lie condition on the equivariance group is needed in order for (the available proofs of) the equivariant Whitehead theorem to hold.

    diff, v12, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 13th 2021

    added brief mentioning of the equivariant triangulation theorem under “Properties” (here)

    diff, v12, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 8th 2021

    added pointer to:

    diff, v15, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeApr 8th 2021

    added brief mentioning (here) that every compact Lie group admits a bi-invariant metric

    diff, v16, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeNov 4th 2021

    I have added (here) the statement that connected compact abelian Lie groups are tori (with reference to Adams 1982) and then statement and proof that compact abelian Lie groups are direct products of tori with finite abelian groups.

    For ease of cross-linking this at other relevant pages, I’ll give this also it’s own little stand-alone page “classification of abelian compact Lie groups”.

    diff, v22, current

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)