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]

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# I have a conjecture/ possibly already a theorem

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