lie groups - Lie Algebra of SO (n) - Mathematics Stack Exchange
Apr 24, 2017 · Welcome to the language barrier between physicists and mathematicians. Physicists prefer to use hermitian operators, while mathematicians are not biased towards …
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 ...
Dimension of SO (n) and its generators - Mathematics Stack …
Nov 18, 2015 · 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 …
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.
Oct 3, 2017 · I have known the data of $\\pi_m(SO(N))$ from this Table: $$\\overset{\\displaystyle\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad\\textbf{Homotopy …
Why $\\operatorname{Spin}(n)$ is the double cover of $SO(n)$?
Dec 16, 2024 · You can let $\text {Spin} (n)$ act on $\mathbb {S}^ {n-1}$ through $\text {SO} (n)$. Since $\text {Spin} (n-1)\subset\text {Spin} (n)$ maps to $\text {SO} (n-1)\subset\text {SO} (n)$, …
Tangent space of Lie group SO(n) - Mathematics Stack Exchange
May 9, 2024 · 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 ...
general topology - The special orthogonal group is a manifold ...
Jun 28, 2014 · yes but $\mathbb R^ {n^2}$ is connected so the only clopen subsets are $\mathbb R^ {n^2}$ and $\emptyset$
The Tuesday Birthday Problem - Mathematics Stack Exchange
In case this is the correct solution: Why does the probability change when the father specifies the birthday of a son? (does it actually change? A lot of answers/posts stated that the statement …
Are $SO(n)\\times Z_2$ and $O(n)$ isomorphic as topological …
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