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SUMMARY:Floris Elzinger
DTSTART:20200714T130000Z
DTEND:20200714T140000Z
DTSTAMP:20260423T035726Z
UID:GOBA/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOBA/1/">Fre
 e orthogonal quantum groups and strong 1-boundedness</a>\nby Floris Elzing
 er as part of Groups\, Operators\, and Banach Algebras Webinar\n\n\nAbstra
 ct\nThe free orthogonal quantum groups\, depending on a parameter matrix Q
 \, form an accessible class of examples of compact quantum groups\, which 
 can be viewed as analogues of both the real orthogonal groups and certain 
 free product groups. In fact\, a particularly well-behaved subclass\, wher
 e the parameter matrix is conjugate to either an identity $I_M$ or standar
 d symplectic $J_{2N}$\, shares many von Neumann algebraic properties with 
 the free groups. A natural question is then whether these objects are dist
 inguishable on the von Neumann algebraic level. Recently\, Brannan and Ver
 gnioux managed to show that in case $Q = I_M$ these operator algebras sati
 sfy a free-probabilistic property called strong 1-boundedness\, which the 
 free group factors do not. Their proof employs techniques from the theory 
 of compact quantum groups\, free probability\, and the quantum analogue of
  Cayley graphs. We will review the necessary notions and explain how the t
 echniques of Brannan and Vergnioux can be extended to also cover the missi
 ng case $Q = J_{2N}$.\n
LOCATION:https://researchseminars.org/talk/GOBA/1/
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