Homotopy groups O(N) and SO(N): $\\pi_m(O(N))$ v.s. $\\pi_m(SO(N))$
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 …
Fundamental group of the special orthogonal group SO(n)
Also, if I'm not mistaken, Steenrod gives a more direct argument in "Topology of Fibre Bundles," but he might be using the long exact sequence of a fibration (which you mentioned).
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 ...
orthogonal matrices - Irreducible representations of $SO (N ...
Sep 21, 2020 · I'm looking for a reference/proof where I can understand the irreps of $SO(N)$. I'm particularly interested in the case when $N=2M$ is even, and I'm really only ...
Dimension of SO (n) and its generators - Mathematics Stack Exchange
Nov 18, 2015 · 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 ...
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 hermitian operators. …
Distinguishing $SU(n)$ from $SO(n)$ - Mathematics Stack Exchange
May 24, 2017 · Suppose that I have a group $G$ that is either $SU(n)$ (special unitary group) or $SO(n)$ (special orthogonal group) for some $n$ that I don't know. Which "questions ...
What is the relationship between SL (n) and SO (n)?
I'm in Linear Algebra right now and we're mostly just working with vector spaces, but they're introducing us to the basic concepts of fields and groups in preparation taking for Abstract Algebra la...
Representation theory of $SO (n)$ - Mathematics Stack Exchange
Regarding the downvote: I am really sorry if this answer sounds too harsh, but math.SE is not the correct place to ask this kind of questions which amounts to «please explain the represnetation …
Diophantus' Lifespan - Mathematics Stack Exchange
"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.