Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
Example: Proof that $\mathrm{Mp}(2, \Bbb R)$ is not a matrix group:…. – Henry T. Horton Oct 2 '12 at 18:03
See also this related discussion on MO:… – Henry T. Horton Oct 2 '12 at 18:05
See also: – commenter Oct 3 '12 at 14:30

There is the metaplactic group, which is the unique connected double cover of the symplectic group.

share|cite|improve this answer

Lie groups are smooth manifolds. They may or may not have matrix representations. For example, ordinary Euclidean space with vector addition is a Lie group.

share|cite|improve this answer
But Euclidean space has a matrix representation, so it is a matrix group. – M Turgeon Oct 2 '12 at 18:11
I misinterpreted the question. It certainly does. The universal cover of $\mathbf{SL}_2(\mathbf{R})$ is a good example. – Luis Costa Oct 2 '12 at 18:18

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.