Lie foliations transversely modeled on nilpotent Lie algebras
Tóm tắt
In this paper, we study on the following two problems of realization for Lie foliations. (1) Which pair of Lie algebras $$(\mathfrak {g},\mathfrak {h})$$ can be realized as a Lie $$\mathfrak {g}$$ -foliation in a closed manifold with the structure Lie algebra $$\mathfrak {h}$$ ? (2) Which pair $$(\mathfrak {g},m)$$ can be realized as a Lie $$\mathfrak {g}$$ -flow in a closed manifold with the structure Lie algebra $${\mathbb {R}}^m$$ ? We give a complete answer to (1) in the case where $$\mathfrak {g}$$ is a nilpotent Lie algebra and give a complete answer to (2) in the case where $$\mathfrak {g}$$ is a nilpotent Lie algebra which has a rational structure.
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