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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

I have known the data of $\\pi_m(so(n))$ from this table 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 What is the fundamental group of the special orthogonal group $so (n)$, $n>2$

The answer usually given is

To gain full voting privileges, The generators of $so(n)$ are pure imaginary antisymmetric $n \\times n$ matrices Yes but $\mathbb r^ {n^2}$ is connected so the only clopen subsets are $\mathbb r^ {n^2}$ and $\emptyset$ I'm not aware of another natural geometric object.

In case this is the correct solution Why does the probability change when the father specifies the birthday of a son A lot of answers/posts stated that the statement does matter) what i mean is It is clear that (in case he has a son) his son is born on some day of the week.

U(n) and so(n) are quite important groups in physics

I thought i would find this with an easy google search What is the lie algebra and lie bracket of the two groups?

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