Date of Award

6-1-2023

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Dissertation/Thesis Chair

Rongwei Yang

Committee Members

Changlong Zhong, Christian Lenart, Antun Milas

Keywords

characteristic polynomial, determinant, Lie algebras, linear algebra, spectral equivalence

Subject Categories

Physical Sciences and Mathematics

Abstract

For a finite dimensional Lie algebra with basis {X1, ..., Xn} wedefine the characteristic polynomial with respect to the adjoint representation using matrix representatives as det (z0*I + z1*ad X1 + ... + zn*ad Xn). Spectral equivalence is defined and used in a new method to classify low dimensional complex solvable Lie algebras. The characteristic polynomial of so-called graphical Lie algebras is also computed.

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