Re: Question on Lie Groups

From: Robin Chapman (rjc_at_ivorynospamtower.freeserve.co.uk)
Date: 01/31/05 

Date: Mon, 31 Jan 2005 08:57:16 +0000

Jannick Asmus wrote:

>
> After a quick look at your argument the question came to my mind whether
> the image of this curve needs to be multiplicatively closed? E.g. if the
> curve is multiplicative, i.e. it enjoys the property of a group
> homomorphism.

Asking whether a curve such as this can be found for all points in
a connected Lie group G is to ask whether the exponential map for G
is surjective. There are such G (ISTR SL_2(R) is one) for which this
is not the case. 

-- 
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
  "Elegance is an algorithm"
    Iain M. Banks, _The Algebraist_

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