The unitary group as a complete invariant for simple unital AF algebras.

Abstract

In 1955, Henry Dye showed that factors with isomorphic unitary groups are in a certain sense isomorphic, provided they are not of type $I\sb{2n}.$ We establish a similar result for simple AF algebras, namely that the unitary group of a simple AF algebra is a complete invariant. Also, there appears to be an error in Dye's paper which allows us to strengthen his result so that it is valid for factors not of type $I\sb2.$