Talk:Central extension

From Wikipedia, the free encyclopedia

I attended a seminar yesterday where the following definition of central extension was given: Let G be a group. The group G' is a central extension of G if there is a normal subgroup H of G' such that H is central (meaning that every element of H commutes with every element in G') and G' / H is isomorphic to G. This seems similar to the definition in the article, except that the article talks only about Lie groups (without using the Lie structure, as far as I can see). Can somebody who knows the stuff confirm this, and possibly update the article if necessary? -- Jitse Niesen 15:43, 5 Feb 2004 (UTC)

Jitse - I put in the textbook definition of central extension. should i delete the old one, which is not very precise (and you are right, you certainly don t need to have a Lie group, although that is most common). or move the old definition somewhere else? i think we should have a separate definition for a central extension to a Lie algebra, too. -lethe

Lethe - I really do not know enough abstract algebra, but I trust you and Charles and have removed the old definition. I also removed the example, which just confused me more by talking about extensions of the Lie algebra. Both the old definition and the example were contributed by an anynomous editor, so removing them seems the only option (they are of course still stored in the page history). It makes the article really short though, and it would be great if you or somebody else could expand it a bit and make the link to Lie groups and the applications in physics. Thanks for the help. -- Jitse Niesen 14:56, 8 Feb 2004 (UTC)

and how do i make the link for center point to the group theoretic definition, instead of the english dictionary definition of the word "center"? (Done -check page history.)

The definition in the article seems suspect ('abelian' too weak, condition that the extension doesn't split too strong).

Charles Matthews 15:46, 5 Feb 2004 (UTC)

By the way, the Lie algebra example is at Galilean transformation. It is probably good for this article, too, but after the definition has been given of central extension of a Lie algebra. There are numerous other examples, though.

Charles Matthews 15:13, 8 Feb 2004 (UTC)

The business about fundamental groups - I'm not really clear why this does give central extensions (this is probably quite well-known, though).

Charles Matthews 10:51, 8 May 2004 (UTC)