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SUMMARY:Paolo Saracco (Université Libre de Bruxelles\, Belgium)
DTSTART:20210531T140000Z
DTEND:20210531T150000Z
DTSTAMP:20260422T175521Z
UID:QGS/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QGS/30/">Glo
 balization for Geometric Partial Comodules</a>\nby Paolo Saracco (Universi
 té Libre de Bruxelles\, Belgium) as part of Quantum Groups Seminar [QGS]\
 n\n\nAbstract\n(based on a joint work [2] with Joost Vercruysse)\n\nThe st
 udy of partial symmetries (partial actions and coactions\, partial represe
 ntations and corepresentations\, partial comodule algebras) is a relativel
 y recent field in continuous expansion and\, therein\, one of the relevant
  questions is the existence and uniqueness of a so-called globalization (o
 r enveloping action). \nFor instance\, in the framework of partial actions
  of groups any global action of a group $G$ on a set induces a partial act
 ion of the group on any subset by restriction. The idea behind the concept
  of globalization of a given partial action is to find a (universal) $G$-s
 et such that the initial partial action can be realized as the restriction
  of this global one.\n\nWe propose here a categorical approach to partial 
 symmetries and the globalization question\, explaining several of the exis
 ting results and\, at the same time\, providing a procedure to construct g
 lobalizations in concrete contexts of interest. Our approach relies on the
  notion of geometric partial comodules\, recently introduced by Hu and Ver
 cruysse [1] in order to describe partial actions of algebraic groups from 
 a Hopf-algebraic point of view.\n\nUnlike classical partial actions\, whic
 h exist only for (topological) groups and Hopf algebras\, geometric partia
 l comodules can be defined over any coalgebra in a monoidal category with 
 pullbacks and they allow to describe phenomena that are out of the reach o
 f the theory of partial (co)actions\, even in the Hopf algebra framework. 
 At the same time\, geometric partial comodules allow to approach in a unif
 ied way partial actions of groups on sets\, partial coactions of Hopf alge
 bras on algebras and partial (co)actions of Hopf algebras on vector spaces
 .\nThus\, the question of studying the existence (and uniqueness) of globa
 lization for geometric partial comodules naturally arises as a unifying wa
 y to address the issue.\n\nReferences:\n\n[1] J. Hu\, J.Vercruysse - Geome
 trically partial actions. Trans. Amer. Math. Soc. 373 (2020)\, no. 6\, 408
 5-4143.\n\n[2] P. Saracco\, J. Vercruysse - Globalization for geometric pa
 rtial comodules. Part I: general theory. Preprint (2021).\n
LOCATION:https://researchseminars.org/talk/QGS/30/
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