BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joost Vercruysse (Université Libre de Bruxelles) DTSTART:20231019T090000Z DTEND:20231019T100000Z DTSTAMP:20260423T035716Z UID:EQuAL/14 DESCRIPTION:Title: G eneralizations of Yetter-Drinfel'd modules and the center construction of monoidal categories\nby Joost Vercruysse (Université Libre de Bruxell es) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nTh is is joint work with Ryan Aziz. A Yetter-Drinfel'd module over a bialgebr a $H$\, is at the same time a module and a comodule over $H$ satisfying a particular compatibility condition. It is well-known that the category of Yetter-Drinfel'd modules (say\, over a finite dimensional Hopf algebra $H$ ) is equivalent to the center of the monoidal category of $H$-(co)modules as well as to the category of modules over the Drinfel'd double of $H$. Ca enepeel\, Militaru and Zhu introduced a generalized version of Yetter-Drin feld modules. More precisely\, they consider two bialgebras $H$\, $K$\, to gether with an bimodule coalgebra $C$ and a bicomodule algebra $A$ over th em. A generalized Yetter-Drinfel'd module in their sense\, is an $A$-modul e that is at the same time a $C$-comodule satisfying a certain compatibili ty condition. Under finiteness conditions\, they showed that these modules are exactly modules of a suitably constructed smash product build out of $A$ and $C$. The aim of this talk is to show how the category of these gen eralized Yetter-Drinfel'd can be obtained as a relative center of the cate gory of $A$-modules\, viewed as a bi-actegory over the categories of $H$-m odules and $K$-modules. Moreover\, we also show how other variations of Ye tter-Drinfel'd modules\, such as anti-Yetter-Drinfel'd modules\, arise as a particular case and we discuss the bicategorical structure that arises t his way.\n LOCATION:https://researchseminars.org/talk/EQuAL/14/ END:VEVENT END:VCALENDAR