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Welcome to the language barrier between physicists and mathematicians 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. 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 $so (n)$, $n>2$ What is the lie algebra and lie bracket of the two groups? The answer usually given is

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

To gain full voting privileges, 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 You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful

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Instead, you can save this post to reference later. U (n) and so (n) are quite important groups in physics I thought i would find this with an easy google search