Algorithms for Finite Dimensional Algebras Over Finite Fields Using Basic Algebras

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Graduate College

Grantor dc:publisher

The University of Arizona.

Year dc:date.issued

2022

Author dc:creator

• Elert, Eric Alan

Advisor dc:contributor.advisor

• Lux, Klaus

Committee members dc:contributor.committeemember

• Pickrell, Douglas
• Xue, Hang
• Kececioglu, John

Statement dc:rights

• Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction, presentation (such as public display or performance) of protected items is prohibited except with permission of the author.

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10150/664987

OAI identifier oai:identifier

oai:repository.arizona.edu:10150/664987