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 ...
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 ...
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 …
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 ...
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...
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. …
group theory - Generators Of $SO (n)$ - Mathematics Stack Exchange
Aug 1, 2024 · I was wondering, for the group $SO(n)$, as far as I understand, the $n\\choose 2$ infinitesimal rotations in the plane spanned by $e_i$ and $e_j$ for $0\\le i<j< ...
matrices - Geodesics on $SO (n)$ - Mathematics Stack Exchange
Jun 11, 2016 · I'm trying to prove the following exercise about the ortogonal symmetric group $SO(n)$. I have been able to prove the first two sections of the exercise but I got ...
Homotopic type of $GL^+ (n)$, $SL (n)$ and $SO (n)$
May 14, 2016 · I don't believe that the tag homotopy-type-theory is warranted, unless you are looking for a solution in the new foundational framework of homotopy type theory. It sure would be an interesting …