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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On Lie algebras of vector fields


Authors: Akira Koriyama, Yoshiaki Maeda and Hideki Omori
Journal: Trans. Amer. Math. Soc. 226 (1977), 89-117
MSC: Primary 57D25; Secondary 58H05
DOI: https://doi.org/10.1090/S0002-9947-1977-0431196-5
MathSciNet review: 0431196
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0431196-5
Keywords: Cores of Lie algebras, multivalued primitive structures
Article copyright: © Copyright 1977 American Mathematical Society