Lie algebra extensions of current algebras on S3

Tosiaki Kori; Yuto Imai

doi:10.1142/S0219887815500875

Lie algebra extensions of current algebras on S³

Tosiaki Kori, Yuto Imai

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

1 Citation (Scopus)

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 language	English
Article number	1550087
Journal	International Journal of Geometric Methods in Modern Physics
Volume	12
Issue number	9
DOIs	https://doi.org/10.1142/S0219887815500875
Publication status	Published - 2015 Oct 1

Keywords

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

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

Access to Document

10.1142/S0219887815500875

Cite this

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