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SUMMARY:Benjamin Anderson-Sackaney (Université de Caen\, France)
DTSTART:20231113T150000Z
DTEND:20231113T160000Z
DTSTAMP:20260422T181410Z
UID:QGS/104
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QGS/104/">To
 pological Boundaries of Representations and Coideals</a>\nby Benjamin Ande
 rson-Sackaney (Université de Caen\, France) as part of Quantum Groups Sem
 inar [QGS]\n\n\nAbstract\nWe will introduce and study quantum analogues of
  Furstenberg-Hamana boundaries of representations of discrete quantum grou
 ps\, where the Furstenberg boundary is the Furstenberg-Hamana boundary of 
 the left regular representation. Our focus is on the GNS representations o
 f idempotent states\, or to put it differently\, the quasi-regular represe
 ntations coming from coideals associated to compact quasi-subgroups. We us
 e their Furstenberg-Hamana boundaries to study (co)amenability properties 
 of such coideals. Then\, we combine our work with recent work of Hataishi 
 and De Ro to settle open problems of Kalantar\, Kasprzak\, Skalski\, and V
 ergnioux for wide classes of quantum groups\, including unimodular discret
 e quantum groups and C*-exact discrete quantum groups. For example\, we pr
 ove that a unimodular discrete quantum group has the unique trace property
  iff it acts faithfully on its Furstenberg boundary.\n\nThis is joint work
  with Fatemeh Khosravi.\n
LOCATION:https://researchseminars.org/talk/QGS/104/
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