On Lie algebras of vector fields

Koriyama, Akira; Maeda, Yoshiaki; Omori, Hideki

doi:10.1090/S0002-9947-1977-0431196-5

On Lie algebras of vector fields
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by Akira Koriyama, Yoshiaki Maeda and Hideki Omori PDF

Trans. Amer. Math. Soc. 226 (1977), 89-117 Request permission

Abstract:

This paper has two purposes. The first is a generalization of the theorem of Pursell-Shanks [10]. Our generalization goes by assuming the existence of a nontrivial core of a Lie algebra. However, it seems to be a necessary condition for the theorems of Pursell-Shanks type. The second is the classification of cores under the assumption that the core itself is infinitesimally transitive at every point. As naturally expected, we have the nonelliptic, primitive infinite-dimensional Lie algebras.

References

Foundations of mechanics

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