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Dissertation/Thesis Abstract

Classification of Five-Dimensional Lie Algebras with One-Dimensional Subalgebras Acting as Subalgebras of the Lorentz Algebra
by Rozum, Jordan, M.S., Utah State University, 2016, 186; 10007630
Abstract (Summary)

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.

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Indexing (document details)
Advisor: Anderson, Ian
Commitee: Fels, Mark, Torre, Charles
School: Utah State University
Department: Mathematics and Statistics
School Location: United States -- Utah
Source: MAI 55/03M(E), Masters Abstracts International
Subjects: Mathematics
Keywords: Homogeneous, Isometry, Lie algebra, Maple, Pseudo-riemannian, Slice
Publication Number: 10007630
ISBN: 978-1-339-44950-0
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