BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Georgy Sharygin DTSTART:20240306T162000Z DTEND:20240306T180000Z DTSTAMP:20260423T041810Z UID:GDEq/106 DESCRIPTION:Title: D eformation quantisation of the argument shift on $U\\mathfrak{gl}(n)$\ nby Georgy Sharygin as part of Geometry of differential equations seminar\ n\nLecture held in room 303 of the Independent University of Moscow.\n\nAb stract\nArgument shift algebras are the commutative subalgebras in the sym metric algebras of a Lie algebra\, generated by the iterated derivations ( in direction of a constant vector field) of Casimir elements in $S\\mathfr ak{gl}(n)$. In particular all these quasiderivations do mutually commute. In my talk I will show that a similar statement holds for the algebra $U\\ mathfrak{gl}(n)$ and its quasiderivations: namely\, I will show that itera ted quasiderivations of the central elements of $U\\mathfrak{gl}(n)$ with respect to a constant quasiderivation do mutually commute. Our proof is ba sed on the existence and properties of "Quantum Mischenko-Fomenko" algebra s\, and (which is worse) cannot be extended to other Lie algebras\, but we believe that the fact that the "shift operator" can be raised to $U\\math frak{gl}(n)$ is an interesting fact.\n LOCATION:https://researchseminars.org/talk/GDEq/106/ END:VEVENT END:VCALENDAR