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- Age problem of father and son - Mathematics Stack Exchange
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 Find age of each
- 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
- Why $\\operatorname{Spin}(n)$ is the double cover of $SO(n)$?
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 $\text {SO} (n-1)\subset\text {SO} (n)$, you could then use the argument directly for $\text {Spin} (n)$, using that $\text {Spin} (3)$ is simply connected because $\text {Spin} (3)\cong\mathbb {S}^3$ I'm not aware of another natural geometric object
- 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
- 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
- How connectedness of $O(n)$ or $SO(n)$ implies the connectedness of . . .
So, the quotient map from one Lie group to another with a discrete kernel is a covering map hence $\operatorname {Pin}_n (\mathbb R)\rightarrow\operatorname {Pin}_n (\mathbb R) \ {\pm1\}$ is a covering map as @MoisheKohan mentioned in the comment I hope this resolves the first question If we restrict $\operatorname {Pin}_n (\mathbb R)$ group to $\operatorname {Spin}_n (\mathbb R
- Prove that the manifold $SO (n)$ is connected
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
- Showing SO(n) is a compact topological group for every n
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