Automorphisms and dilation theory of triangular UHF algebras

TL;DR

This paper investigates the structure and automorphisms of triangular UHF subalgebras, revealing their properties, automorphism groups, and the nature of their semicrossed products, contributing to operator algebra theory.

Contribution

It introduces new examples of triangular UHF subalgebras with specific properties and describes their automorphism groups and semicrossed products.

Findings

Automorphisms form a semidirect product of an abelian and a torsion-free group.

Triangular UHF subalgebras have the Dirichlet and Ando properties.

Structural results on automorphism groups are established.

Abstract

We study the triangular subalgebras of UHF algebras which provide new examples of algebras with the Dirichlet property and the Ando property. This in turn allows us to describe the semicrossed product by an isometric automorphism. We also study the isometric automorphism group of these algebras and prove that it decomposes into the semidirect product of an abelian group by a torsion free group. Various other structure results are proven as well.