BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alex Frei DTSTART:20210517T140000Z DTEND:20210517T150000Z DTSTAMP:20260423T052756Z UID:GOBA/27 DESCRIPTION:Title: Re lative Cuntz-Pimsner algebras: a complete description of their lattice of gauge-invariant ideals\nby Alex Frei as part of Groups\, Operators\, a nd Banach Algebras Webinar\n\n\nAbstract\nWe give a new\, systematic appro ach to the gauge-invariant uniqueness theorem describing all relative Cunt z-Pimsner algebras\,\nand whence revealing a complete description of their gauge-invariant ideal lattice.\n\nFor this we start with a swift introduc tion to C*-correspondences\, in particular drawing a comparison to Fell bu ndles.\n\nContinuing\, we provide a slightly deeper analysis of covariance s as well as their relation to kernels and quotients. With these observati ons at hand\, we introduce the relevant reduction leading us to a suitable parametrization of relative Cuntz-Pimsner algebras\, and so revealing a c omplete description of their gauge-invariant ideal lattice.\nOur parametri zation is a heuristic analog of Katsura's originally obtained one.\n\nWith this at hand\, we arrive at the gauge-invariant uniqueness theorem\, for all arbitrary gauge-equivariant representations.\n\nFrom here we move on t o the analysis part of the program. We compute the covariances in the case of the Fock representation and its quotients. As a result\, we derive tha t the parametrization of relative Cuntz-Pimsner algebras introduced above is also classifying. In other words\, we obtain a complete and intrinsic p icture of the lattice of quotients\, and equivalently of their lattice of gauge-invariant ideals.\n\nIf time permits\, we finish off with the next c hapter on their induced Fell bundles and dilations\, as already investigat ed by Schweizer.\n LOCATION:https://researchseminars.org/talk/GOBA/27/ END:VEVENT END:VCALENDAR