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What is the fundamental group of the special orthogonal group $so (n)$, $n>2$ Are $so (n)\times z_2$ and $o (n)$ isomorphic as topological groups The answer usually given is

Welcome to the language barrier between physicists and mathematicians I'm particularly interested in the case when $n=2m$ is even, and i'm really only. Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators

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. I have known the data of $\\pi_m(so(n))$ from this table The generators of $so(n)$ are pure imaginary antisymmetric $n \\times n$ matrices

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. To gain full voting privileges,

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 I'm looking for a reference/proof where i can understand the irreps of $so(n)$

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