BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dan Petersen (Stockholms universitet) DTSTART:20200811T090000Z DTEND:20200811T100000Z DTSTAMP:20260423T004136Z UID:operad/6 DESCRIPTION:Title: L ie\, associative and commutative quasi-isomorphism\nby Dan Petersen (S tockholms universitet) as part of operad pop-up\n\n\nAbstract\nLet A and A ' be commutative dg algebras over Q. There are two a priori different noti ons of what it means for them to be quasi-isomorphic: one could ask for a zig-zag of quasi-isomorphisms in the category of commutative dg algebras\, or a zig-zag in the larger category of not necessarily commutative dg alg ebras. Our first main result is that these two notions coincide. The secon d main result is Koszul dual to the first\, and states that if two dg Lie algebras over Q have quasi-isomorphic universal enveloping algebras\, then the derived completions of the two dg Lie algebras are quasi-isomorphic. The latter result is new even for classical Lie algebras concentrated in d egree zero. Both results have immediate consequences in rational homotopy theory. (Joint with Campos\, Robert-Nicoud\, Wierstra)\n LOCATION:https://researchseminars.org/talk/operad/6/ END:VEVENT END:VCALENDAR