Lie algebra extensions of current algebras on S3

Tosiaki Kori, Yuto Imai

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    Abstract

    An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.

    Original languageEnglish
    Article number1550087
    JournalInternational Journal of Geometric Methods in Modern Physics
    Volume12
    Issue number9
    DOIs
    Publication statusPublished - 2015 Oct 1

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    Keywords

    • current algebra
    • Infinite-dimensional Lie algebras
    • Lie algebra extensions
    • quaternion analysis

    ASJC Scopus subject areas

    • Physics and Astronomy (miscellaneous)

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