Talk:Compact group

This is a test -- don't read it. Michael Hardy 17:58, 27 Aug 2004 (UTC)

Damn. Too late. -- Fropuff 04:40, 29 September 2006 (UTC)

Non-compact groups

Could it be useful to give a few examples of non-compact groups (i.e. the Lorentz-group)? To give a better understanding wether a group is compact or not.

Non Lie conpact groups.

I would like an example (or pointer to) a compact topological group that is not a Lie Group.

NormHardy 05:09, 15 July 2007 (UTC)

See the section "Further examples". Arcfrk 02:53, 18 July 2007 (UTC)

Finite groups are Lie groups?

Unless there's some degenerate definition of a Lie group I'm not familiar with, finite groups are not Lie groups - they are not locally homeomorphic to R^n or C^n. I've removed this and put it further down as a set of (rather trivial) further examples of compact topological groups. —Preceding unsigned comment added by 41.185.115.52 (talk) 18:11, 14 January 2011 (UTC)

Is this right?

The first section after the introduction, Compact groups, reads as follows:

" Lie groups form a class of topological groups, and the compact Lie groups have a particularly well-developed theory. Basic examples of compact Lie groups include

• the circle group T and the torus groups Tⁿ,
• the orthogonal groups O(n), the special orthogonal group SO(n) and its covering spin group Spin(n),
• the unitary group U(n) and the special unitary group SU(n),
• the compact forms of the exceptional Lie groups: G₂, F₄, E₆, E₇, and E₈,

The classification theorem of compact Lie groups states that up to finite extensions and finite covers this exhausts the list of examples (which already includes some redundancies). This classification is described in more detail in the next subsection. "

But even something as simple as the product of a compact nonabelian Lie group (necessarily of dimension ≥ 3) with the circle group seems to be a counterexample.

Is this correct? Can someone who is knowledgeable in this subject please please clarify this? Thank you. 2601:200:C000:1A0:2C05:9DCB:77A0:C778 (talk) 01:18, 9 May 2022 (UTC)

References