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Welcome to the language barrier between physicists and mathematicians I'm not aware of another natural geometric object. Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators

What is the fundamental group of the special orthogonal group $so (n)$, $n>2$ I have a potentially simple question here, about the tangent space of the lie group so (n), the group of orthogonal $n\times n$ real matrices (i'm sure this can be. The answer usually given is

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

To gain full voting privileges, 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

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