Inner Extensions of Automorphisms of Irrational Rotation Algebras to AF-Algebras

Abstract

Let $A_\theta$ be an irrational rotation algebra. In the present paper we will show that automorphisms of $A_\theta$ with some properties can be extended to inner automorphisms of an AF-algebra. In other words, there are a monomorphism $\rho$ of $A_\theta$ into an AF-algebra $B$ and a unitary element $w\in B$ such that $\rho(\alpha(x))=w\rho(x)w^*$ for any $x\in A_\theta$.