BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexei Pirkovskii (HSE University\, Moscow) DTSTART:20210304T140000Z DTEND:20210304T143000Z DTSTAMP:20260421T121128Z UID:cats2021/14 DESCRIPTION:Title: Flat locally convex modules beyond the metrizable case\nby Alexei Pi rkovskii (HSE University\, Moscow) as part of Additive categories between algebra and functional analysis\n\n\nAbstract\nWe begin by surveying class ical results (due to Johnson\, Helemskii\, and Sheinberg) on amenable Bana ch algebras and flat Banach modules. In particular\, we discuss Helemskii- Sheinberg's theorem which states that a Banach algebra A is Johnson amenab le if and only if its unitization is a flat Banach A-bimodule. Next we loo k at some possible extensions of these concepts to more general locally co nvex algebras and modules. The "naive" generalization of the notion of a f lat Banach module to the nonmetrizable setting turns out to be not very us eful. We suggest a modified definition\, and we show how it works in concr ete situations. As an application\, we give a characterization of amenable co-echelon algebras obtained in our recent perprint with Krzysztof Piszcz ek. Curiously\, the nonmetrizable case requires some essentially new tools (as compared to the Banach case)\, not only from analysis\, but also from homological algebra (t-structures and their hearts).\n LOCATION:https://researchseminars.org/talk/cats2021/14/ END:VEVENT END:VCALENDAR