- lie groups - Lie Algebra of SO (n) - Mathematics Stack Exchange
Welcome to the language barrier between physicists and mathematicians Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators So for instance, while for mathematicians, the Lie algebra $\mathfrak {so} (n)$ consists of skew-adjoint matrices (with respect to the Euclidean inner product on $\mathbb {R}^n$), physicists prefer to multiply them
- Fundamental group of the special orthogonal group SO(n)
Question: What is the fundamental group of the special orthogonal group $SO (n)$, $n>2$? Clarification: The answer usually given is: $\mathbb {Z}_2$ But I would like
- Prove that the manifold $SO (n)$ is connected
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- Homotopy groups O(N) and SO(N): $\\pi_m(O(N))$ v. s. $\\pi_m(SO(N))$
I have known the data of $\\pi_m(SO(N))$ from this Table: $$\\overset{\\displaystyle\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad\\textbf{Homotopy groups of
- Dimension of SO (n) and its generators - Mathematics Stack Exchange
The generators of $SO(n)$ are pure imaginary antisymmetric $n \\times n$ matrices How can this fact be used to show that the dimension of $SO(n)$ is $\\frac{n(n-1
- Are $SO(n)\\times Z_2$ and $O(n)$ isomorphic as topological groups?
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- Why $\\operatorname{Spin}(n)$ is the double cover of $SO(n)$?
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- orthogonal matrices - Irreducible representations of $SO (N . . .
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