Talk:Symplectic group

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Contents 1 Real or complex entries 2 Fundamental groups 3 Simplicity and center 4 Expert attention needed

[edit] Real or complex entries

Symmetric matrices are defined for complex entries only in the Wikipedia. --Andres.

Are we talking about Symmetric matrix or Symplectic matrix here? Phys

Sorry, I mean symplectic matrices. --Andres

[edit] Fundamental groups

Does anyone know which of the symplectic groups are simply connected? I know that Sp(1) and Sp(2, C) are, and that Sp(2, R) is not. I suspect this holds for all n, but I have no proof. -- Fropuff 16:04, 2004 May 20 (UTC)

Nevermind. What I said is correct, I know how to prove it now. -- Fropuff 14:28, 2004 May 28 (UTC)

[edit] Simplicity and center

I'm trying to pull together information on matrix groups and was wondering if someone could answer the following questions.

• When is Sp(2n,F) simple?
• What is the center of Sp(2n,F)?

In particular I'm interested in the case when F is finite, however if the results include R,C or all fields it would be useful to include them. TooMuchMath 17:47, 15 April 2006 (UTC)

[edit] Expert attention needed

Can someone please flag this page as "in need of attention by an expert"? The last section is rather rough, and in particular, it implies that "O(3) is isomorphic SU(2)", which is wrong. Thanks. 98.223.87.110 (talk) 06:17, 10 May 2008 (UTC)