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What is the fundamental group of the special orthogonal group $so (n)$, $n>2$ The answer usually given is Welcome to the language barrier between physicists and mathematicians Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian. The generators of $so(n)$ are pure imaginary antisymmetric $n \\times n$ matrices To gain full voting privileges, 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 It's fairly informal and talks about paths in a very I have known the data of $\\pi_m(so(n))$ from this table If he has two sons born on tue and sun he will mention tue 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. 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? 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