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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

4 votes
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Number of submodules in $\wedge^2 V$ and $S^2V$ isomorphic to $\mathfrak{g}$

Let $\mathfrak{g}$ be a simple complex Lie algebra. Let $\mathfrak{g}\subset\mathfrak{so}(V)$ be an orthogonal irreducible representation. It can be shown that the number of $\mathfrak{g}$-submodule …
Anton Galaev's user avatar
2 votes

Lie groups acting transitively (and isometrically) on anti de Sitter spaces

In my paper Isometry groups of Lobachevskian spaces, similarity transformation groups of Euclidean spaces and Lorentzian holonomy groups. Rend. Circ. Mat. Palermo (2) Suppl. No. 79 (2006), 87–97. I …
Anton Galaev's user avatar