Let $M$ be a von Neumann algebra having a cyclic vector in $\mathcal{H}$, is the fixed point subalgebra under the flip automorphism on $M\otimes M$ has a cyclic vector in $\mathcal{H}\otimes \mathcal{H}$. Furthermore, what is the commutant of the fixed point algebra under flip?
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1$\begingroup$ What do you think the fixed point subalgebra is in this case? Can you then perform a calculation with the cyclic vector for $M$? $\endgroup$– Matthew DawsCommented Apr 12, 2019 at 9:55
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$\begingroup$ I tried with your idea before not really getting significant what we want to prove $\endgroup$– user136400Commented Apr 12, 2019 at 13:43
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