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Results tagged with lie-groups
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user 9962
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
1
vote
Representations of Lorentz group
The Lorenz group is essentially a semidirect product of $SL(2,\mathbb C)$ and a four dimensional abelian group. (I am only considering the connected component of identity, but that is not a big deal. …
- 741
3
votes
0
answers
40
views
Generating $K$-types of a $(\mathfrak g,K)$-module for $K$ disconnected
Let $G$ be a real reductive Lie group, let $K$ be a maximal compact subgroup of $G$, and let $V$ be a $(\mathfrak g,K)$-module. For $\sigma\in\widehat{K}$ we denote the $\sigma$-isotypic component of …
- 741
5
votes
Lie algebras to classify Lie groups
Here is an answer from a different point of view: every connected Lie group is almost a semidirect product of a semisimple Lie group (Levi factor) and a connected solvable normal Lie subgroup (its sol …
- 741