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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

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What is the fundamental group of the special orthogonal group $so (n)$, $n>2$ I thought i would find this with an easy google search The answer usually given is

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I have known the data of $\\pi_m(so(n))$ from this table 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

A father's age is now five times that of his first born son Six year from now, the old man's age will be only three times that his first born son The son lived exactly half as long as his father is i think unambiguous Almost nothing is known about diophantus' life, and there is scholarly dispute about the approximate period in which he lived.

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