Let $M$ be a von Neumann algebra acting in a Hilbert space $H$, and let $\rho$ be a representation of a group $G$ on a Hilbert space $K$. Define $M\rtimes_\rho G$ to be a von Neumann algebra acting in the Hilbert space $H\bar\otimes K$ generated by $$x\otimes\rho(g), \quad x\in M, g\in G$$ Is the von Neumann algebra $M\rtimes_\rho G$ studied?
$\begingroup$
$\endgroup$
3
asked Nov 11, 2018 at 11:28
-
2$\begingroup$ but what is your multiplication? the trivial one leads to $M \otimes VN^*(G)$ !? $\endgroup$– hänselNov 11, 2018 at 12:26
-
$\begingroup$ @hänsel Do you know somewhere which this kind of crossed product is studied with non trivial multiplication? $\endgroup$– Meisam Soleimani MalekanNov 11, 2018 at 12:48
-
$\begingroup$ @MeisamSoleimaniMalekan: with $G \subset Aut(M)$ you can get a non-trivial multiplication via the usual crossed product: see Chapter X in Takesaki's book Theory of Operator Algebras II. $\endgroup$– Sebastien PalcouxNov 12, 2018 at 9:50
Add a comment
|