I am not very well read so this may already exist as a theorem. If not, try to prove it, or disprove it.(adsbygoogle = window.adsbygoogle || []).push({});

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)

[/tex]

Here's a simple example:

SU(2) is the maximal compact subgroup of [tex]

Sl\left( {2,\mathbb{C}} \right)

[/tex]

And [tex]

SU(2)_\mathbb{C} \cong Sl\left( {2,\mathbb{C}} \right)

[/tex]

**Physics Forums - The Fusion of Science and Community**

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

Loading...

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 |

**Physics Forums - The Fusion of Science and Community**