On lie algebras of vector fields

Akira Koriyama; Yoshiaki Maeda; Hideki Omori

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

On lie algebras of vector fields

Akira Koriyama, Yoshiaki Maeda, Hideki Omori

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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.

Original language	English
Pages (from-to)	89-117
Number of pages	29
Journal	Transactions of the American Mathematical Society
Volume	226
DOIs	https://doi.org/10.1090/S0002-9947-1977-0431196-5
Publication status	Published - 1977

Keywords

Cores of Lie algebras
Multivalued primitive structures

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-1977-0431196-5

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AU - Omori, Hideki

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AB - 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.

KW - Cores of Lie algebras

KW - Multivalued primitive structures

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JF - Transactions of the American Mathematical Society

ER -

On lie algebras of vector fields

Abstract

Keywords

ASJC Scopus subject areas

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