Date of Award

Spring 1994

Abstract

This paper deals with universal $C\sp\*$-algebras generated by matricial relations on the generators, for example, the universal $C\sp\*$-algebra with generators $a\sb{ij}, 1 \leq i,j \leq n$, subject to the condition that the matrix ($a\sb{ij}$) be normal and have spectrum in a designated compact subset ${\cal K}$ of the complex plane.

The main thrust of the paper is to compute the K-groups of some of these $C\sp\*$-algebras and to determine when they contain non-trivial projections. In the above example, we show that the K-groups of the algebra coincide with the topological K-groups of the set ${\cal K}$. We show, in general, that if the algebra has a multiplicative linear functional, then the K-theory is independent of n, when the matricial constraints are fixed.

It is also shown that if the constraints are fixed and ${\cal A}\sb n$ is the algebra with $n\sp2$ generators, then the tensor product of ${\cal A}\sb n$ with the algebra $M\sb n$ of complex n x n matrices is isomorphic to the free product of ${\cal A}\sb1$ with $M\sb n$.

Also in the example above, the algebra contains no non-trivial projections when n is not less than the number of connected components of ${\cal K}$. These results have also been extended to include the case in which the constraints are in several variables.

Document Type

Dissertation

First Advisor

Donald Hadwin

Department or Program

Mathematics

Degree Name

Doctor of Philosophy

Download

Share

COinS