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. 4633.
Copyright for this work is retained by the student. If you have any questions regarding the inclusion of this work in the Digital Commons, please email us at .