### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

^{3}

*International Journal of Geometric Methods in Modern Physics*,

*12*(9), [1550087]. https://doi.org/10.1142/S0219887815500875

**Lie algebra extensions of current algebras on S ^{3}
.** / Kori, Tosiaki; Imai, Yuto.

Research output: Contribution to journal › Article

^{3}',

*International Journal of Geometric Methods in Modern Physics*, vol. 12, no. 9, 1550087. https://doi.org/10.1142/S0219887815500875

^{3}International Journal of Geometric Methods in Modern Physics. 2015 Oct 1;12(9). 1550087. https://doi.org/10.1142/S0219887815500875

}

TY - JOUR

T1 - Lie algebra extensions of current algebras on S3

AU - Kori, Tosiaki

AU - Imai, Yuto

PY - 2015/10/1

Y1 - 2015/10/1

N2 - 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.

AB - 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.

KW - current algebra

KW - Infinite-dimensional Lie algebras

KW - Lie algebra extensions

KW - quaternion analysis

UR - http://www.scopus.com/inward/record.url?scp=84943581895&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84943581895&partnerID=8YFLogxK

U2 - 10.1142/S0219887815500875

DO - 10.1142/S0219887815500875

M3 - Article

AN - SCOPUS:84943581895

VL - 12

JO - International Journal of Geometric Methods in Modern Physics

JF - International Journal of Geometric Methods in Modern Physics

SN - 0219-8878

IS - 9

M1 - 1550087

ER -