4
votes
Accepted
$p$-torsion in fundamental group of Lie group.
First, the fundamental group of a connected Lie group is abelian and finitely generated.
Secondly, any finitely generated abelian group is the fundamental group of a connected Lie group.
To see the ...
- 128k
1
vote
$p$-torsion in fundamental group of Lie group.
It's a fundamental result that if $G$ is a connected Lie group then the universal covering map $\widetilde{G} \to G$ has kernel a central subgroup of $\widetilde{G}$ isomorphic to $\pi_1(G)$, giving a ...
- 407k
1
vote
Accepted
Inducing a Lie algebra action from a Lie group action
The intuition behind your question does not really work out. The problem is that the isotropy representation of $G$ is already obtained by differentiating the map $x\mapsto \rho(g)(x)$ in the point $p$...
- 19.7k
1
vote
Accepted
(locally) symmetric spaces where every conformal transformation is an isometry
It is proven in Corollary 1 of
Nagano, Tadashi, The conformal transformation on a space with parallel Ricci tensor, J. Math. Soc. Japan 11, 10-14 (1959). ZBL0089.17201.
that if $M$ is a connected ...
- 92.2k
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