BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Atabey Kaygun (Istanbul Technical University\, Turkey) DTSTART:20260706T150000Z DTEND:20260706T160000Z DTSTAMP:20260602T192900Z UID:ENAAS/180 DESCRIPTION:Title: Birational Normal Forms for Kac--Moody Algebras\nby Atabey Kaygun (Ist anbul Technical University\, Turkey) as part of European Non-Associative A lgebra Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/780318 1064\n\nAbstract\nThe classical Gel'fand--Kirillov conjecture posits that the quotient division algebra of an enveloping algebra is a Weyl skew fiel d. The conjecture is known for finite-dimensional solvable Lie algebras\, hence for Borel subalgebras of finite-dimensional semisimple Lie algebras. The conjecture also holds for their \\(q\\)-deformations at generic \\(q\ \). In this talk\, I will explain a Kac--Moody version of the birational p roblem\, where the correct normal form is no longer a single Weyl algebra but a pair of Weyl-polynomial Borel models glued by a smash-biproduct stru cture. Our main result identifies the two Borel halves of a Kac--Moody alg ebra associated with a generalized Cartan matrix \\(C\\) of corank \\(\\el l\\) with the birational model \\(A_{n-\\ell\,n}\\otimes k[t_1\,\\ldots\,t _\\ell]\\)\, where \\(A_{n-\\ell\,n}\\) is the corresponding rectangular W eyl algebra. The proof goes through controlled Ore localizations and Carta n-bound generalized Weyl algebras\, making the birational transformation e xplicit instead of passing directly to the maximal localization. The coran k of \\(C\\) determines the number of residual polynomial variables. I wil l also explain how the same mechanism extends to Drinfeld--Jimbo quantizat ions by replacing Weyl algebras with their \\(q\\)-analogues.\n LOCATION:https://researchseminars.org/talk/ENAAS/180/ URL:https://us02web.zoom.us/j/7803181064 END:VEVENT END:VCALENDAR