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Results tagged with lie-groups
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user 3634
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
5
votes
$H_2$ of a simply connected Lie group vanishes
One way to do this is to use a very nice theorem of Weingram:
if $G$ is finitely generated, then no nontrivial map $\Omega S^{2n+1} \to K(G, 2n)$ can factor through a finite-dimensional CW complex.
…
- 12.5k
1
vote
Compact Lie group action on non-Hausdorff (but CGWH) space with Hausdorff quotient
How about $X=\{ a,b,x,y\}$ with nontrivial open sets $\{a,b\}$ and $\{ x,y\}$ and $G= Z/2$, discrete.
The action exchanges $a$ with $ b$ and $x$ with $y$.
- 12.5k
13
votes
2
answers
3k
views
Left and right eigenvalues
A quaternionic matrix $A$ gives rise to a
function $\mathbb{H}^n \to \mathbb{H}^n$
given by $x \mapsto A \cdot x$. This is real linear,
but not complex- or quaternionic-linear
(in general) if we co …
- 12.5k