Representations of McLain Groups
Date
2016-06
Authors
Izadi, Mohammadali
Journal Title
Journal ISSN
Volume Title
Publisher
Faculty of Graduate Studies and Research, University of Regina
Abstract
Basic 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.
Description
A Thesis
Submitted to the Faculty of Graduate Studies and Research
In Partial Fulfillment of the Requirements
For the Degree of
Doctor of Philosophy
In
Mathematics,
University of Regina. iv, 54 p.