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Results tagged with lie-groups
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user 4008
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
34
votes
Accepted
Which groups have only real and quaternionic irreducible representations?
An irreducible representation is real or quaternionic precisely when its
character is real-valued. By the Peter-Weyl theorem all characters are
real-valued precisely when every element in the group is …
- 22.6k
15
votes
Accepted
Is a polynomial group law on $\mathbb{R}^n$ automatically nilpotent?
This is true and is in "Michel Lazard: Sur la nilpotence de certains groupes algébriques, Comptes Rendus, vol 241, 1955, 1687--1689"
- 22.6k
12
votes
Torsion for Lie algebras and Lie groups
I don't know the answer to the actual question but here is a situation which
should be similar but simpler. Consider an integral polynomial group law $G$,
i.e., a group scheme structure on the affine …
- 22.6k
7
votes
Accepted
sub-tori of a torus, generated by 1-dimensional subgroup
The key to solving both problems is the use of the following two facts: 1) Any
closed subgroup of $T^n$ is the intersection of the kernels of characters of
$T^n$, i.e., continuous group homomorphisms …
- 22.6k