Morita-Äquivalenzen in der algorithmischen Darstellungstheorie

This thesis contributes to the algorithmic representation theory of sporadic simple groups. We augment the condensation method by allowing to condense with an arbitrary primitive idempotent of a linear character of the condensation subgroup. To this end we introduce the necessary algorithms theoretically and practically to treat tensor products of modules and induced modules. We furthermore investigate how the encountered generation problem can be dealt with and suggest two new ways to overcome it. Firstly we present new generating sets for the condensed algebra, which are often small enough to be computationally tractable. We also introduce a method which enables us to decrease the size of such a generating set by verifying the redundancy of generators without prior condensation. Secondly we develop a new criterion intheory and practice for proving that a subset of the condensed algebra is a set of generators. In the final chapter of this thesis we combine our new condensation methods with our knowledge of generating systems for the condensed algebra to compute the 2- and 3-modular character tables of the sporadic simple Fischer group Fi22 as part of the modular atlas project.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2005

Author dc:creator

• Noeske, Felix

Contributors dc:contributor

• Hiß, Gerhard

• info:eu-repo/classification/ddc/510
• Darstellungstheorie
• Sporadische Gruppe
• Kondensation <Mathematik>
• Mathematik
• Brauertafel
• Fi22
• Erzeugnisproblem

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

ger

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-121815%22

OAI identifier oai:identifier

oai:publications.rwth-aachen.de:60087