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Results tagged with lie-groups
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user 81169
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
2
votes
Counterexamples to Margulis Normal subgroup theorem in rank 1
Also interesting in this context is the existence of compact complex surfaces whose universal cover is the ball and admitting an holomorphic map onto a Riemann surface with connected fibers. The kerne …
- 411
2
votes
A question on linear groups
In fact the subgroup generated by $SO(n)$ and $tSO(n)t^{-1}$ is certainly connected by arc (as the union of images of arc-connected spaces $SO(n)^k, k\in \bf N$ by the obvious product map) So it is an …
- 11.2k
2
votes
Hamiltonian potential invariant under lie group action?
If $V$ is a vector field on $M$, its lift to $T^*M$ is a Hamiltonian vector field with hamiltonian function $V$ (viewed as a linear function on the fibers). And if the vector field $V$ is $G$-invarian …
- 375
2
votes
Classifying compact homogeneous Kähler manifolds
For the first question, there is another (paerhaps more conceptual) proof using the so called moment map of symplectic geometry. This proof, probably due to Souriau, is to consider the so-called momen …
- 411