UHF flows and the flip automorphism
Kishimoto, A.
arXiv, 0011140 / Harvested from arXiv
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.
Publié le : 2000-11-20
Classification:  Mathematics - Operator Algebras,  Mathematical Physics
@article{0011140,
     author = {Kishimoto, A.},
     title = {UHF flows and the flip automorphism},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0011140}
}
Kishimoto, A. UHF flows and the flip automorphism. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0011140/