Villadsen algebras are singly generated

TL;DR

This paper proves that Villadsen algebras and a broader class of simple unital AH algebras with diagonal maps are singly generated, expanding understanding of their algebraic structure.

Contribution

It establishes that Villadsen algebras, previously not known to be singly generated, are in fact singly generated, along with a broader class of AH algebras.

Findings

Villadsen algebras are singly generated.

Any simple unital AH algebra with diagonal maps is singly generated.

This expands the class of known singly generated C*-algebras.

Abstract

We show that Villadsen algebras, which are not Z-stable, are singly generated. More generally, we show that any simple unital AH algebra with diagonal maps is singly generated.