I vaguely recall learning once that there are Lie groups which are not
isomorphic to any matrix groups, and I think one example was the
universal cover of GL(n).  I would like to know some more about this. 
Is my recollection correct about the cover of GL(n)?  If so, why can't
that group be realized as a matrix group?  What other Lie groups are
not matrix groups?  Where can I learn more?

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Clarification of Question by lethe-ga on 09 Mar 2005 08:40 PST

I know that Spin(3)=SU(2) and Spin(4)=SU(2)xSU(2), and I think there
might be a few more like that.  But is a general Spin(n) a matrix
group?

Here are a couple of places to learn more:

http://mathworld.wolfram.com/LieGroup.html

http://en.wikipedia.org/wiki/Lie_group