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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.
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
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
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
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