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## Classification of Five-Dimensional Lie Algebras with One-Dimensional Subalgebras Acting as Subalgebras of the Lorentz Algebra

<p> Motivated by A. Z. Petrov's classification of four-dimensional Lorentzian metrics, we provide an algebraic classification of the isometry-isotropy pairs of four-dimensional pseudo-Riemannian metrics admitting local slices with five-dimensional isometries contained in the Lorentz algebra. A purely Lie algebraic approach is applied with emphasis on the use of Lie theoretic invariants to distinguish invariant algebra-subalgebra pairs. This method yields an algorithm for identifying isometry-isotropy pairs subject to the aforementioned constraints.</p>

Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:10007630 |

Date | 24 February 2016 |

Creators | Rozum, Jordan |

Publisher | Utah State University |

Source Sets | ProQuest.com |

Language | English |

Detected Language | English |

Type | thesis |

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