Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I have a conjecture/ possibly already a theorem

  1. Dec 20, 2008 #1
    I am not very well read so this may already exist as a theorem. If not, try to prove it, or disprove it.

    Let G be a compact group over the reals, then the maximally compact subgroup of the complexification of G is just G over the reals.

    That is the maximally compact subgroup of [tex]G_\mathbb{C}[/tex] is just [tex]
    G\left( \mathbb{R} \right)

    Here's a simple example:

    SU(2) is the maximal compact subgroup of [tex]
    Sl\left( {2,\mathbb{C}} \right)

    And [tex]
    SU(2)_\mathbb{C} \cong Sl\left( {2,\mathbb{C}} \right)
  2. jcsd
  3. Dec 22, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    definitions would be nice. or does maximal compact mean just that? no larger compact subgroup exists? or no larger proper compact subgroup?
  4. Dec 22, 2008 #3


    User Avatar
    Science Advisor
    Homework Helper

    a few minutes web search reveals, without even knowing wjhat these things mean, that any compact group is a maximal compact of its chevalley complexification.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - conjecture possibly already Date
Is it possible to convert 2D coordinates of point to 3D form ? Jun 9, 2014
Poincare conjecture May 30, 2012
Poincare conjecture Mar 2, 2010
Poincare conjecture. Jan 28, 2007
Complete Solution of Poincare Conjecture Jul 28, 2006