BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Benjamin Anderson-Sackaney (Université de Caen\, France) DTSTART:20221018T140000Z DTEND:20221018T150000Z DTSTAMP:20260422T175348Z UID:QGS/65 DESCRIPTION:Title: Rel ative Amenability\, Amenability\, and Coamenability of Coideals\nby Be njamin Anderson-Sackaney (Université de Caen\, France) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nAmenability is a deeply studied prope rty of groups\, with many interesting reformulations and connections to th e operator algebraic aspects of groups. For example\, the reduced $C^*$-al gebra $C^*_r(G)$ of a discrete group has a unique tracial state if and onl y if there are no non-trivial amenable normal subgroups. This\, among othe r related results\, makes it apparent that the structure of the amenable s ubgroups of $G$ contains important information about $C^*_r(G)$. For a qua ntum group $\\mathbb{G}$\, an appropriate analogue of a subgroup is a coid eal $N\\subseteq L^\\infty(\\mathbb{G})$. We will present notions of relat ive amenability\, amenability\, and coamenability for coideals of discrete and compact quantum groups motivated by "relativizations" of amenability and coamenability of a subgroup of a group. We will discuss the known rela tionships between these formally distinct notions and their relevance to c ertain properties of the reduced $C^*$-algebras of discrete quantum groups .\n LOCATION:https://researchseminars.org/talk/QGS/65/ END:VEVENT END:VCALENDAR