BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Paolo Saracco (Université Libre de Bruxelles) DTSTART:20210615T133000Z DTEND:20210615T143000Z DTSTAMP:20260423T052830Z UID:itaca/6 DESCRIPTION:Title: Gl obalization for geometric partial comodules\nby Paolo Saracco (Univers ité Libre de Bruxelles) as part of ItaCa Fest 2021\n\n\nAbstract\nThe stu dy of partial symmetries (e.g. partial dynamical systems\, (co)actions\, ( co)representations\, comodule algebras) is a relatively recent research ar ea in continuous expansion\, whose origins can be traced back to the study of C*-algebras generated by partial isometries. One of the central questi ons in the field is the existence and uniqueness of a so-called globalizat ion or enveloping (co)action.\n\nIn the framework of partial actions of gr oups\, any global action of a group on a set induces a partial action of t he group on any subset by restriction. The idea behind the concept of glob alization of a given partial action is to find a (universal) global action such that the initial partial action can be realized as the restriction o f this global one. The importance of this procedure is testified by the nu merous globalization results already existing in the literature which\, ho wever\, are based on some ad hoc constructions\, depending on the nature o f the objects carrying the partial action.\n\nWe propose here a unified ap proach to globalization in a categorical setting\, explaining several of t he existing results from the literature and\, at the same time\, providing a procedure to construct globalizations in concrete contexts of interest. Our approach relies on the notion of geometric partial comodules (recentl y introduced by Hu and Vercruysse in [HV]) which –unlike classical parti al actions\, that exist only for (topological) groups and Hopf algebras– can be defined over any coalgebra in an arbitrary monoidal category with pushouts.\n\n[HV] J. Hu\, J. Vercruysse\, Geometrically partial actions. T rans. Amer. Math. Soc. 373 (2020)\, no. 6\, 4085–4143.\n\n[PJ] P. Saracc o\, J. Vercruysse\, Globalization for geometric partial comodules. Preprin t (2020).\n LOCATION:https://researchseminars.org/talk/itaca/6/ END:VEVENT END:VCALENDAR