Date

2019

Document Type

Dissertation

Degree

Doctor of Philosophy

Department

Mathematics

First Adviser

Johnson, David L.

Abstract

The index of a Lie algebra $\mathfrak{g}$ is defined by $\ind \g=\min_{f\in \mathfrak{g}^*} \dim (\ker (B_f))$, where $f$ is an element of the linear dual $\mathfrak{g}^*$ and $B_f(x,y)=f([x,y])$ is the associated skew-symmetric Kirillov form. We develop a broad general framework for the explicit construction of regular (index realizing) functionals for seaweed subalgbras of $\mathfrak{gl}(n)$ and the classical Lie algebras in type-A and type-C. (Type-B and type-D are also considered - though subtle cases remain open).) Until now, this significant problem has remained open in all cases.

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