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Welcome to the language barrier between physicists and mathematicians It's fairly informal and talks about paths in a very Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators

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What is the fundamental group of the special orthogonal group $so (n)$, $n>2$ 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 The answer usually given is

The generators of so(n) s o (n) are pure imaginary antisymmetric n×n n × n matrices

How can this fact be used to show that the dimension of so(n) s o (n) is n(n−1) 2 n (n 1) 2 I know that an antisymmetric matrix has n(n−1) 2 n (n 1) 2 degrees of freedom, but i can't take this idea any further in the demonstration of the proof To gain full voting privileges, I have known the data of $\\pi_m(so(n))$ from this table

I'm not aware of another natural geometric object. You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do i get it

Instead, you can save this post to reference later.