BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dominic Verdon (University of Bristol\, UK) DTSTART:20210927T140000Z DTEND:20210927T150000Z DTSTAMP:20260422T181116Z UID:QGS/35 DESCRIPTION:Title: A c ovariant Stinespring theorem\nby Dominic Verdon (University of Bristol \, UK) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nWe will intr oduce a finite-dimensional covariant Stinespring theorem for compact quant um groups. Let G be a compact quantum group\, and let T:= Rep(G) be the ri gid C*-tensor category of finite-dimensional continuous unitary representa tions of G. Let Mod(T) be the rigid C*-2-category of cofinite semisimple f initely decomposable T-module categories. We show that finite-dimensional G-C*-algebras (a.k.a C*-dynamical systems) can be identified with equivale nce classes of 1-morphisms out of the object T in Mod(T). For 1-morphisms X: T -> M1\, Y: T -> M2\, we show that covariant channels between the corr esponding G-C*-algebras can be 'dilated' to isometries t: X -> Y \\otimes E\, where E: M2 -> M1 is some 'environment' 1-morphism. Dilations are uniq ue up to partial isometry on the environment\; in particular\, the dilatio n minimising the quantum dimension of the environment is unique up to a un itary. When G is a compact group this implies and generalises previous cov ariant Stinespring-type theorems.\n\nWe will also discuss some results rel ating to rigid C*-2-categories\, including that any connected semisimple r igid C*-2-category is equivalent to Mod(T) for some rigid C*-tensor catego ry T. (Here semisimple means not just semisimplicity of Hom-categories but also idempotent splitting for 1-morphisms\, direct sums for objects\, etc .)\n\nThis talk is based on the paper arXiv:2108.09872.\n LOCATION:https://researchseminars.org/talk/QGS/35/ END:VEVENT END:VCALENDAR