Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - February 1993 - Volume 36, Issue 01  

Research Article

Classification of limits of triangular matrix algebras

A. Hopenwassera1 and S. C. Powera2

a1 Department of Mathematics University of Alabama Tuscaloosa, AL 35487, USA

a2 Department of Mathematics University of Lancaster Lancaster LA1 4YL, England

Abstract

Let Tn be the operator algebra of upper triangular n × n complex matrices. Three families of limit algebras of the form lim (Tnk) are classified up to isometric algebra isomorphism: (i) the limit algebras arising when the embeddings Tnk→Tnk+1, are alternately of standard and refinement type; (ii) limit algebras associated with refinement embeddings with a single column twist; (iii) limit algebras determined by certain homogeneous embeddings. The last family is related to certain fractal like subsets of the unit square.

(Received February 21 1991)