BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andrey Lazarev (Lancaster University\, UK) DTSTART:20240715T150000Z DTEND:20240715T160000Z DTSTAMP:20260423T021126Z UID:ENAAS/80 DESCRIPTION:Title: C ohomology of Lie coalgebras\nby Andrey Lazarev (Lancaster University\, UK) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nAs sociated to a Lie algebra g and a g-module M is a standard complex C*(g\,M ) computing the cohomology of g with coefficients in M\; this classical co nstruction goes back to Chevalley and Eilenberg of the late 1940s. Shortly afterwards\, it was realized that this cohomology is an example of a deri ved functor in the category of g-modules. The Lie algebra g can be replace d by a differential graded Lie algebra and M – with a dg g-module with the same conclusion. Later\, a deep connection with Koszul duality was un covered in the works of Quillen (late 1960s) and then Hinich (late 1990s). In this talk I will discuss the cohomology of (dg) Lie coalgebras with co efficients in dg comodules. The treatment is a lot more delicate\, undersc oring how different Lie algebras and Lie coalgebras are (and similarly the ir modules and comodules). A definitive answer can be obtained for so-call ed conilpotent Lie coalgebras (though not necessarily conilpotent comodule s). If time permits\, I will also discuss some topological applications.\n LOCATION:https://researchseminars.org/talk/ENAAS/80/ END:VEVENT END:VCALENDAR