Classification of limits of triangular matrix algebras

Abstract

Let T n be the operator algebra of upper triangular n × n complex matrices. Three families of limit algebras of the form lim (T nk ) are classified up to isometric algebra isomorphism: (i) the limit algebras arising when the embeddings T nk →T nk+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.