On lie algebras of vector fields

Akira Koriyama, Yoshiaki Maeda, Hideki Omori

    Research output: Contribution to journalArticlepeer-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 languageEnglish
    Pages (from-to)89-117
    Number of pages29
    JournalTransactions of the American Mathematical Society
    Volume226
    DOIs
    Publication statusPublished - 1977 Jan 1

    Keywords

    • Cores of Lie algebras
    • Multivalued primitive structures

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

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