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What is the fundamental group of the special orthogonal group $so (n)$, $n>2$ What is the lie algebra and lie bracket of the two groups? The answer usually given is

Welcome to the language barrier between physicists and mathematicians I thought i would find this with an easy google search Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian.

The generators of $so(n)$ are pure imaginary antisymmetric $n \\times n$ matrices

I've found lots of different proofs that so(n) is path connected, but i'm trying to understand one i found on stillwell's book naive lie theory It's fairly informal and talks about paths in a very I have known the data of $\\pi_m(so(n))$ from this table To gain full voting privileges,

If he has two sons born on tue and sun he will mention tue U(n) and so(n) are quite important groups in physics

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