[Summer time:] UK, Portugal: 16:00; Spain, Italy, France, etc.: 17:00
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177. 06/07/2026 Atabey Kaygun (Istanbul Technical University, Turkey)
Title: Birational Normal Forms for Kac--Moody Algebras
Abstract: The classical Gel'fand--Kirillov conjecture posits that the quotient division algebra of an enveloping algebra is a Weyl skew field. 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 problem, 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 structure. Our main result identifies the two Borel halves of a Kac--Moody algebra associated with a generalized Cartan matrix C of corank l with the birational model A_{n-l,n} \otimes k[t_1,...,t_l], where A_{n-l,n} is the corresponding rectangular Weyl algebra. The proof goes through controlled Ore localizations and Cartan-bound generalized Weyl algebras, making the birational transformation explicit instead of passing directly to the maximal localization. The corank of C determines the number of residual polynomial variables. I will also explain how the same mechanism extends to Drinfeld--Jimbo quantizations by replacing Weyl algebras with their q-analogues.
Future talks:
178. 13/07/2026 Marco Castelli (University of Salento, Italy)
179. 20/07/2026 Yannic Vargas (CUNEF University, Spain)
180. 27/07/2026 Marijana Butorac (University of Rijeka, Croatia)
181. 03/08/2026 Elad Paran (The Open University of Israel, Israel)
182. 10/08/2026 Diogo Diniz (Federal University of Campina Grande, Brazil)
183. 17/08/2026 Lực Ta (University of Pittsburgh, USA)
184. 24/08/2026 Jethro van Ekeren (Institute of Pure and Applied Mathematics, Brazil)
185. 31/08/2026 Veronika Pedić (University of Zagreb, Croatia)
186. 07/09/2026 Aliaksandr Hancharuk (Jilin University, China)
187. 14/09/2026 Mihalis Maliakas (National and Kapodistrian University of Athens, Greece)
188. 21/09/2026 Geoffrey Powell (University of Angers, France)
189. 28/09/2026 Frédéric Patras (Côte d'Azur University, France)
190. 05/10/2026 Silvia Properzi (Vrije Universiteit Brussel, Belgium)
191. 12/10/2026 István Heckenberger (Philipps University Marburg, Germany)
192. 19/10/2026 Simon Goodwin (University of Birmingham, UK)
193. 26/10/2026 Joost Vercruysse (Université Libre de Bruxelles, Belgium)
194. 02/11/2026 Diego Aranda-Orna (University of Oviedo, Spain)
195. 09/11/2026 Inna Entova-Aizenbud (Ben Gurion University of the Negev, Israel)
196. 16/11/2026 Anupam Singh (Indian Institute of Science Education and Research, India)
197. 23/11/2026 Sofiane Bouarroudj (New York University Abu Dhabi, United Arab Emirates)
198. 30/11/2026 Matevž Miščič (University of Ljubljana, Slovenia)
199. 07/12/2026 Ernesto Spinelli (Sapienza University of Rome, Italy)
200. 14/12/2026 Maria Matushko (Steklov Mathematical Institute of RAS, Russia)
Ivan Kaygorodov • Salvatore Siciliano • Mykola Khrypсhenko • Jobir Adashev