Re: Question on Lie Groups

From: Jannick Asmus (jannick.news_at_web.de)
Date: 01/31/05 

Date: Mon, 31 Jan 2005 15:38:25 +0100

On 31.01.2005 09:57, Robin Chapman wrote:
> 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.
>

Sure. Thanks, Robert, I had exactly this fact in mind when I was writing
my concern.

Even if the curve is patched by pieces of multiplicatively closed curves
(modulo a left multiplication with a group element), using pathwise
connectedness seems to me to be misleading. The main assertion still
needs to be shown.

J.

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