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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
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Lie group action on a finite dimensional flat manifold
Consider a finite dimensional flat Riemannian manifold $M$ quotiented by an action of a finite dimensional Lie group $G$, giving rise to the quotient $Q$.
First, assume that the action is isometric. …
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An algorithm to compare two representations of a simple Lie algebra?
I have two representations of a simple (complex or real) finite-dimensional Lie algebra $S$, both given in terms of their structure constants on a given basis.
the first one is the adjoint represent …