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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 operators

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 If he has a son & daughter both born on tue he will mention the son, etc. I'm not aware of another. U(n) and so(n) are quite important groups in physics

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