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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeJun 20th 2011
   • (edited Jun 20th 2011)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI added a reference to a paper of Connes and Rovelli (1994) and a link (in [[modular theory]]) to * MathOverflow question [tomita-takesaki-versus-frobenuis-where-is-the-similarity](http://mathoverflow.net/questions/68270/tomita-takesaki-versus-frobenuis-where-is-the-similarity) where André Henriques asks about some Connes philosophy. But André quotes in explaining the background to his question, that in full generality there is a homomorphism from imaginary line into the 2-group of invertible bimodules of the given von Neumann algebra $M$, which *in the presence of state* lifts to the homomorphism into $Aut(M)$. I learned just the case when there is a state, and am delighted to hear that this is just a strengthening of some categorical structure which exists even more generally. If somebody is familiar or can dig more on that general case, it would be nice to have such categorical picture in the $n$Lab entry [[modular theory]].

   I added a reference to a paper of Connes and Rovelli (1994) and a link (in modular theory) to

   • MathOverflow question tomita-takesaki-versus-frobenuis-where-is-the-similarity

   where André Henriques asks about some Connes philosophy. But André quotes in explaining the background to his question, that in full generality there is a homomorphism from imaginary line into the 2-group of invertible bimodules of the given von Neumann algebra $M$, which in the presence of state lifts to the homomorphism into $Aut(M)$. I learned just the case when there is a state, and am delighted to hear that this is just a strengthening of some categorical structure which exists even more generally. If somebody is familiar or can dig more on that general case, it would be nice to have such categorical picture in the $n$Lab entry modular theory.