UHF flows and the flip automorphism

Abstract

A UHF flow is an infinite tensor product type action of the reals on a UHF algebra $A$ and the flip automorphism is an automorphism of $A\otimes A$ sending $x\otimes y$ into $y\otimes x$. If $α$ is an inner perturbation of a UHF flow on $A$, there is a sequence $(u_n)$ of unitaries in $A\otimes A$ such that $α_t\otimes α_t(u_n)-u_n$ converges to zero and the flip is the limit of $\Ad u_n$. We consider here whether the converse holds or not and solve it with an additional assumption: If $A\otimes A\cong A$ and $α$ absorbs any UHF flow $β$ (i.e., $α\otimesβ$ is cocycle conjugate to $α$), then the converse holds; in this case $α$ is what we call a universal UHF flow.