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SUMMARY:Braided tensor product of dynamical von Neumann algebras - Jacek K
 rajczok (Vrije Universiteit Brussel)
DTSTART:20241205T111000Z
DTEND:20241205T115000Z
UID:TALK218641@talks.cam.ac.uk
DESCRIPTION:Whenever locally compact group acts on von Neumann algebras M\
 ,N\, it gives rise to a canonical "diagonal" action on their tensor produc
 t M$\\bar{\\otimes}$N. This is no longer true\, if we consider actions of 
 locally compact quantum groups (which include "coactions" of discrete grou
 ps). Nonetheless\, not all is lost. If the quantum group acting on von Neu
 mann algebras M\,N is quasi-triangular (i.e. it is equipped with an R-matr
 ix)\, then one can form a twisted version of tensor product\, called the b
 raided tensor product M$\\overline{\\boxtimes}$N. This is a new von Neuman
 n algebra which contains M\,N as subalgebras and which carries a canonical
  action of G. As a special case\, G can be taken to be the Drinfeld double
  of some (quantum) group H\, then action of G=D(H) on M\,N amounts to comp
 atible actions of H and its dual quantum group. I will discuss constructio
 n of M$\\overline{\\boxtimes}$N\, its extension to the case of a bicharact
 er\, some examples and properties. This is a joint work with Kenny De Comm
 er.
LOCATION:Seminar Room 1\, Newton Institute
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