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 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
I'm not aware of another natural geometric object. A son had recently visited his mom and found out that the two digits that form his age (eg :24) when reversed form his mother's age (eg Later he goes back to his place and finds out that this whole 'age' reversed process occurs 6 times And if they (mom + son) were lucky it would happen again in future for two more times. U (n) and so (n) are quite important groups in physics I thought i would find this with an easy google search
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