Compression Limit Algebras

TL;DR

This paper investigates the structure of direct limits of upper triangular matrix algebras with non-* extendible embeddings, identifying their C*-envelopes through specific representations and providing illustrative examples.

Contribution

It introduces a new approach to understanding the C*-envelope of limit algebras formed by non-* extendible embeddings of upper triangular matrices.

Findings

Identified the C*-envelope for certain limit algebras

Constructed explicit representations of the limit algebra

Provided examples illustrating the theory

Abstract

This paper studies direct limits of full upper triangular matrix algebras with embeddings which are not *-extendible. A representation of the limit algebra is found so that the generated C*-algebra is the C*-envelope. Some examples are described.