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Welcome to the language barrier between physicists and mathematicians What is the lie algebra and lie bracket of the two groups? 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 thought i would find this with an easy google search 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 Each of 20 families selected to take part in a treasure hunt consist of a mother, father, son, and daughter Assuming that they look for the treasure in pairs that are randomly chosen from the 80

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

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