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arxiv: math/0011140 · v1 · submitted 2000-11-20 · 🧮 math.OA · math-ph· math.MP

UHF flows and the flip automorphism

classification 🧮 math.OA math-phmath.MP
keywords alphaotimesflowautomorphismflipbetaconverseholds
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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.

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