Tuesday, April 5, 2022 at 2:00 p.m. (sharp)

PhD Candidate: Saied Sorkhou

Supervisor: Joe Repka

Thesis title: Levi Decomposable Subalgebras of Classical Lie Algebras with Regular

Simple Levi Factor

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This thesis describes and characterizes a significant class of subalgebras of the classical Lie algebras, namely those which are Levi decomposable with regular and simple Levi factor, with select exceptions. Such subalgebras are entirely determined by their Levi factors and radicals. The possible Levi factors are well-established in the literature and so the contribution of this thesis is a characterization of the radicals. The radicals naturally decompose into nontrivial and trivial components. The nontrivial component is found to be fully classified by subsets of the parent root system and Weyl group. However, a classification of the trivial component requires solving the open problem of classifying solvable subalgebras of classical Lie algebras. Nonetheless, this thesis establishes a criterion on the trivial components for determining when two such subalgebras are conjugate. This thesis also briefly explores the ramifications of relaxing

simplicity of the Levi factor to allow for semisimplicity.

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A draft of the thesis is available here: thesis_draft_Feb_23_2022

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