Algorithms for Finite Dimensional Algebras Over Finite Fields Using Basic Algebras
type: CreativeWork
description: This dissertation describes algorithms for computing information about finite dimensional associative algebra over a finite field. In particular, we provide algorithms for computing a basis, the lattice of two-sided ideals, the center, and the unit group for a finite dimensional associative algebra over a finite field.The primary strategy employed is to first compute the basic algebra using the techniques described by J. Carlson and G. Matthews in [CM06], then perform computations in the basic algebra where possible. The algorithms described in the dissertation have been implemented in GAP as a package called Basic Algebras from Matrix generators by the author. Timings for this implementation are provided.
abstract: This dissertation describes algorithms for computing information about finite dimensional associative algebra over a finite field. In particular, we provide algorithms for computing a basis, the lattice of two-sided ideals, the center, and the unit group for a finite dimensional associative algebra over a finite field.The primary strategy employed is to first compute the basic algebra using the techniques described by J. Carlson and G. Matthews in [CM06], then perform computations in the basic algebra where possible. The algorithms described in the dissertation have been implemented in GAP as a package called Basic Algebras from Matrix generators by the author. Timings for this implementation are provided.
author: Elert, Eric Alan
language: en
license: http://rightsstatements.org/vocab/InC/1.0/
date published: 2022
date modified: 2026-07-24T00:57:45Z
provider: University of Arizona
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: The University of Arizona.

PropertyValue
property ID: Handle
value: http://hdl.handle.net/10150/664987