Talk:Analytic subgroup

Analytic subgroup is an important mathematical concept in Lie theory.

One possibility is to add this concept to the article Lie group, but that article is in my opinion already to long.

The main contribution of this (short) article is that it explains an important mathematical concept. If anybody wants to know what an analytic subgroup is, the answer is given in the article!

This article can be expanded with connections to several other Lie group subjects, such as Lie's theorems. Pierreback 12:42, 13 July 2007 (UTC)

This alternative definition should be included: "A subgroup of an analytic group G which is a submanifold in G is called an analytic subgroup" Pierreback 13:13, 13 July 2007 (UTC)


 * Problem here: it is not true even for 1-parameter subgroups that Lie subalgebras of dimension one are in bijective correspondence with the 1-parameter analytic subgroups as defined here. The typical 1-parameter subroup of a 2-torus is dense. Charles Matthews 10:07, 23 September 2007 (UTC)


 * These definitions are taken from Anthony Knapp: Lie groups beyond an introduction, second edition, pages 71-72. He also writes that this definition allows analytic subgroups which are not closed. Perhaps the problem is what definition of regular one uses. This should be included in the article. Pierreback 14:51, 23 September 2007 (UTC)