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150. 15/12/2025 Cristina Draper (University of Málaga, Spain)
Title: Revisiting simple Lie algebras from the view of the grading group
Abstract: In this talk, we discuss the role of gradings on Lie algebras and how they can be used to obtain suitable models for a wide range of structures, including simple, solvable, and nilpotent Lie algebras. We introduce the notion of a generalized group algebra, which provides a flexible framework for describing graded algebras in full generality. Although this concept may at first appear too broad to be useful in the specific context of Lie algebras, we shall show how naturally it applies by examining several illustrative examples. A central theme will be the use of the grading group to gain insight into structural properties of the underlying Lie algebra. For instance, viewing so(8) as a generalized group algebra sheds light on its spin representations and on the phenomenon of triality. More broadly, this perspective greatly simplifies the construction of orthonormal bases, as in the case of g_2. Finally, we show that this approach renders the computation of brackets in Lie algebras obtained via graded contractions essentially immediate. This leads to vast families of high-dimensional nonsimple Lie algebras with distinctive structural features, obtained from the exceptional simple Lie algebras through the Tits construction.
Future talks:
----. 22/12/2025 XX Non-Associative Day in Online´25
151. 05/01/2025 Mateo Tomašević (University of Zagreb, Croatia)
152. 12/01/2026 Ramón González Rodríguez (University of Vigo, Spain)
153. 19/01/2026 Dimitar Grantcharov (University of Texas at Arlington, USA)
154. 26/01/2026 Bernardo Leite da Cunha (University of Santiago de Compostela, Spain)
155. 02/02/2026 Zahra Nazemian (University of Graz, Austria)
156. 09/02/2026 Hans Cuypers (Eindhoven University of Technology, Netherlands)
157. 16/02/2026 Davide Ferri (University of Torino, Italy)
158. 23/02/2026 Saikat Goswami (Institute for Advancing Intelligence, India)
159. 02/03/2026 Solomon Vishkautsan (Tel-Hai Academic College, Israel)
160. 09/03/2026 Lucia Bagnoli (Sapienza University of Rome, Italy)
161. 16/03/2026 Carsten Dietzel (University of Caen Normandy, France)
162. 23/03/2026 István Heckenberger (Philipps University Marburg, Germany)
163. 30/03/2026 Willian Franca (Federal University of Juiz de Fora, Brazil)
164. 06/04/2026 Rong Tang (Jilin University, China)
165. 13/04/2026 Maria Ferrara (University of Campania Luigi Vanvitelli, Italy)
166. 20/04/2026 Michael Lau (Laval University, Canada)
167. 27/04/2026 Abdenacer Makhlouf (University of Haute Alsace, France)
168. 04/05/2026 Per Bäck (Mälardalen University, Sweden)
170. 18/05/2026 Ágota Figula (University of Debrecen, Hungary)
171. 25/05/2026 Andrés Pérez-Rodríguez (University of Santiago de Compostela, Spain)
172. 01/06/2026 Geoffrey Powell (University of Angers, France)
173. 08/06/2026 Ivan Dimitrov (Queen’s University, Canada)
174. 15/06/2026 Rinat Kashaev (University of Geneva, Switzerland)
177. 06/07/2026 Atabey Kaygun (Istanbul Technical University, Turkey)
178. 13/07/2026 Marco Castelli (University of Salento, Italy)
180. 27/07/2026 Marijana Butorac (University of Rijeka, Croatia)
184. 24/08/2026 Jethro van Ekeren (Institute of Pure and Applied Mathematics, Brazil)
Ivan Kaygorodov • Salvatore Siciliano • Mykola Khrypсhenko • Jobir Adashev