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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

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

The generators of $so(n)$ are pure imaginary antisymmetric $n \\times n$ matrices The question really is that simple Prove that the manifold $so(n) \\subset gl(n, \\mathbb{r})$ is connected It is very easy to see that the elements of $so(n)$ are.

I'm not aware of another natural geometric object. 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. Yes but $\mathbb r^ {n^2}$ is connected so the only clopen subsets are $\mathbb r^ {n^2}$ and $\emptyset$

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Upvoting indicates when questions and answers are useful What's reputation and how do i get it Instead, you can save this post to reference later. U(n) and so(n) are quite important groups in physics