Date of Award:
Master of Science (MS)
Mathematics and Statistics
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.
Rozum, Jordan, "Classification of Five-Dimensional Lie Algebras with One-Dimensional Subalgebras Acting as Subalgebras of the Lorentz Algebra" (2015). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 4633.
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