Date of Award
Bachelor of Science
We investigate and classify the Lorentzian geometries on a variety of finite-dimensional Lie algebras. For a given Lie algebra, we first classify Lorentzian scalar products up to a notion of equivalence determined by a change of basis induced by an automorphism (or symmetry) of the underlying Lie algebra. We then use the classification of Lorentzian scalar products to find and classify those scalar products which correspond to algebraic Ricci solitons ( or algebraic Ricci soliton structures for the Lie algebra). A complete classification of Lorentzian scalar products and algebraic Ricci soliton structures is provided for a number of Lie algebras of dimensions three, four, and six.
Walker, Sabrina C., "Geometric Structures on Lie Algebras" (2017). Theses & Honors Papers. 542.