Talk:Lie subgroup

Many references that I have checked do not require Lie subgroups to be closed. Warner's definition (in Foundations of Differentiable Manifolds and Lie Groups) is a Lie group homomorphism &phi; : H &rarr; G such that &phi; is a 1-1 immersion. This seems to be the more common definition in at least the books that I own. We should be careful to note the various definitions. -- Fropuff 03:46, 2005 Mar 24 (UTC)

Agreed. This is however related to how one wishes to state the three basic theorems of Lie. How do we do on that front?

Charles Matthews 09:04, 24 Mar 2005 (UTC)

Definition
It isn't clear that there is a universal definition. For example


 * A subset H of a Lie group G is called a subgroup (more precisely, a Lie subgroup) if H is a subgroup of the abstract group and a submanifold of the analytic manifold.

This is from http://eom.springer.de/l/l058590.htm. If there is no agreement on definitions, the article should note that. Charles Matthews (talk) 14:58, 8 February 2010 (UTC)