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 $\alpha$ is an inner perturbation of a UHF flow on $A$, there is a sequence $(u_n)$ of unitaries in $A\otimes A$ such that ${\alpha }_t\otimes {\alpha }_t(u_n)-u_n$ 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 $\alpha$ absorbs any UHF flow $\beta$ (i.e., $\alpha \otimes \beta$ is cocycle conjugate to $\alpha$), then the converse holds; in this case $\alpha$ is what we call a universal UHF flow.

18 pages

References in corpus (1)

• Examples of one-parameter automorphism groups of UHF algebras

Cited by in corpus (2)

• On a categorical framework for classifying C*-dynamics up to cocycle conjugacy
• Rokhlin dimension: absorption of model actions