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I'm new to Lie Groups, but all the examples I found are matrix groups. Can someone show a non-matrix Lie group?

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    Example: http://en.wikipedia.org/wiki/Metaplectic_group. Proof that $\mathrm{Mp}(2, \Bbb R)$ is not a matrix group: http://concretenonsense.wordpress.com/2009/07/10/a-lie-group-which-isnt-a-matrix-group/.2012-10-02
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    See also this related discussion on MO: http://mathoverflow.net/questions/64195/when-is-a-finite-dimensional-real-or-complex-lie-group-not-a-matrix-group2012-10-02
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    See also: http://math.stackexchange.com/q/1296442012-10-03

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