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- 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
- Prove that the manifold $SO (n)$ is connected
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- Help with a proof that SO (n) is path-connected.
I've found lots of different proofs that SO(n) is path connected, but I'm trying to understand one I found on Stillwell's book "Naive Lie Theory" It's fairly informal and talks about paths in a very
- 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
- Showing SO(n) is a compact topological group for every n
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- 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
- 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
- Tangent space of Lie group SO(n) - Mathematics Stack Exchange
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
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