Faculty of Graduate Studies and Research, University of Regina
Representations of McLain Groups
Abstract
dc:description.abstractBasic modules of McLain groups are defined and investigated. These are a (possibly infinite dimensional) generalization of Andre’s basic modules of the multiplicative group of upper triangular square matrices over a finite field with 1’s on the main diagonal. The ring R need not be finite or commutative and modules of a McLain group are allowed to be infinite dimensional over an arbitrary field F. The set , totally ordered by , is allowed to be infinite. We show that distinct basic modules are disjoint, determine the dimension of the endomorphism algebra of a basic module, find when a basic module is irreducible, and we study the problem of finding a decomposition of a basic module as direct sum of irreducible submodules.
Degree
thesis:*- Name thesis:degree_name
- Doctor of Philosophy (PhD)
- Level thesis:degree_level
- Doctoral -- first
- Discipline thesis:degree_discipline
- Mathematics
- Grantor dc:publisher
- Faculty of Graduate Studies and Research, University of Regina
- Year dc:date.issued
- 2016
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Izadi, Mohammadali
- Advisor dc:contributor.advisor
-
- Szechtman, Fernando
- Committee members dc:contributor.committeemember
-
- Herman, Allen
- Velez, Maria
- Gilligan, Bruce
Rights
- Language dc:language.iso
- en
Identifiers
dc:identifier.*- OAI identifier oai:identifier
- oai:uregina.scholaris.ca:10294/7654