### Abstract

The Lie algebra isomorphism between su(1,1) × su(1,1) and o(2,2) is used to obtain a list of subalgebras of the latter. The resulting list of 32 subalgebras is then examined on a case by case basis to see if each can be the Lie algebra of the holonomy group of a neutral metric in four dimensions. The conclusions, taken in conjunction with previously known results, furnish a classification of such Lie subalgebras of o(2,2), with only one case remaining unresolved.

Original language | English |
---|---|

Pages (from-to) | 2266-2284 |

Number of pages | 19 |

Journal | Journal of Mathematical Physics |

Volume | 42 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2001 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Journal of Mathematical Physics*,

*42*(5), 2266-2284. https://doi.org/10.1063/1.1362284

**The holonomy Lie algebras of neutral metrics in dimension four.** / Ghanam, Ryad; Thompson, G.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 42, no. 5, pp. 2266-2284. https://doi.org/10.1063/1.1362284

}

TY - JOUR

T1 - The holonomy Lie algebras of neutral metrics in dimension four

AU - Ghanam, Ryad

AU - Thompson, G.

PY - 2001/5

Y1 - 2001/5

N2 - The Lie algebra isomorphism between su(1,1) × su(1,1) and o(2,2) is used to obtain a list of subalgebras of the latter. The resulting list of 32 subalgebras is then examined on a case by case basis to see if each can be the Lie algebra of the holonomy group of a neutral metric in four dimensions. The conclusions, taken in conjunction with previously known results, furnish a classification of such Lie subalgebras of o(2,2), with only one case remaining unresolved.

AB - The Lie algebra isomorphism between su(1,1) × su(1,1) and o(2,2) is used to obtain a list of subalgebras of the latter. The resulting list of 32 subalgebras is then examined on a case by case basis to see if each can be the Lie algebra of the holonomy group of a neutral metric in four dimensions. The conclusions, taken in conjunction with previously known results, furnish a classification of such Lie subalgebras of o(2,2), with only one case remaining unresolved.

UR - http://www.scopus.com/inward/record.url?scp=0035532268&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035532268&partnerID=8YFLogxK

U2 - 10.1063/1.1362284

DO - 10.1063/1.1362284

M3 - Article

VL - 42

SP - 2266

EP - 2284

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 5

ER -