### Abstract

An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S^{1} to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S^{3} 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 | |

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)

## Fingerprint Dive into the research topics of 'Lie algebra extensions of current algebras on S<sup>3</sup>'. Together they form a unique fingerprint.

## Cite this

Kori, T., & Imai, Y. (2015). Lie algebra extensions of current algebras on S

^{3}*International Journal of Geometric Methods in Modern Physics*,*12*(9), [1550087]. https://doi.org/10.1142/S0219887815500875