European Non-Associative Algebra Seminar
Activity: Monday, 15:00 (UTC+0)
[Winter time:] UK, Portugal: 15:00; Spain, Italy, France, etc.: 16:00
For e-mail notifications of talks, please register your e-mail HERE.
A special issue dedicated to European Non-Associative Algebra Seminar will be published in
114. 07/04/2025 Jari Desmet (Ghent University, Belgium)
Title: Jordan algebras and automorphism groups of Matsuo algebras
Abstract: Primitive axial algebras of Jordan type half were introduced by Jonathan Hall, Felix Rehren and Sergey Shpectorov in 2015, generalizing Jordan algebras by requiring that their idempotents satisfy the Peirce decomposition. More specifically, primitive axial algebras of Jordan type ½ are commutative non-associative algebras generated by idempotents a such that their multiplication operators Lₐ are diagonalizable with eigenvalues {1,0,½}, such that the fusion laws V₁ = ⟨a⟩, V₀² ⊆ V₀, V₀V_{½} ⊆ V_{½} and V_{½}² ⊆ V₀ ⊕ V₁ hold, where V_λ is the λ-eigenspace of Lₐ. The most well-known examples of this class of algebras are either Jordan algebras or Matsuo algebras, certain non-associative algebras related to 3-transposition groups that Atsushi Matsuo discovered while studying vertex operator algebras. In this talk, we will sketch how one can distinguish these two classes in terms of their automorphism groups. In particular, primitive axial algebras of Jordan type half with large automorphism groups are automatically Jordan while the automorphism groups of non-Jordan Matsuo algebras are usually finite, with one infinite family of exceptions.
Future talks:
115. 14/04/2025 Giovanna Carnovale (University of Padua, Italy)
116. 21/04/2025 Mikhail Kotchetov (Memorial University, Canada)
117. 28/04/2025 Mikhail Ignatyev (HSE University, Russia)
118. 05/05/2025 Geoffrey Janssens (Catholic University of Louvain, Belgium)
119. 12/05/2025 Charles Young (University of Hertfordshire, UK)
120. 19/05/2025 Sue Sierra (University of Edinburgh, UK)
121. 26/05/2024 Simone Blumer (University of Vienna, Austria)
122. 02/06/2025 Marco Farinati (University of Buenos Aires, Argentina)
123. 09/06/2025 Nikita Safonkin (Leipzig University, Germany)
124. 16/06/2025 Brais Ramos Pérez (University of Santiago de Compostela, Spain)
125. 23/06/2025 Agata Pilitowska (Warsaw University of Technology, Poland)
126. 30/06/2025 Vincenzo Nardozza (University of Bari Aldo Moro, Italy)
127. 07/07/2025 Tuan Pham (University of Edinburgh, UK)
128. 14/07/2025 Elkin Quintero Vanegas (Federal University of Amazonas, Brazil)
129. 21/07/2025 Sebastiano Argenti (University of Basilicata, Italy)
130. 28/07/2025 Zohreh Ravanpak (West University of Timisoara, Romania)
131. 04/08/2025 Alan Guimarães (Federal University of Rio Grande do Norte, Brazil)
132. 11/08/2025 Abror Khudoyberdiyev (Institute of Mathematics, Uzbekistan)
133. 18/08/2025 Sachin Sharma (Indian Institute of Technology Kanpur, India)
134. 25/08/2025 Johan Richter (Blekinge Institute of Technology, Sweden)
135. 01/09/2025 Irene Paniello (University of Zaragoza, Spain)
136. 08/09/2025 Iván Ruiz Campos (University of Málaga, Spain)
137. 15/09/2025 Paolo Saracco (Vrije Universiteit Brussel, Belgium)
138. 22/09/2025 Abdenacer Makhlouf (University of Haute Alsace, France)
139. 29/09/2025 Nishant Rathee (IISER Mohali, India)
140. 06/10/2025 Dijana Ilišević (University of Zagreb, Croatia)
141. 13/10/2025 Ilja Gogić (University of Zagreb, Croatia)
142. 20/10/2025 Victor Roca i Lucio (Paris Cité University, France)
143. 27/10/2025 Michiel Smet (Ghent University, Belgium)
144. 03/11/2025 Xiaomin Tang (Heilongjiang University, China)
145. 10/11/2025 Ginevra Giordani (University of L'Aquila, Italy)
146. 17/11/2025 Miguel Gómez Lozano (University of Málaga, Spain)
150. 15/12/2025 Cristina Draper (University of Málaga, Spain)
Organizers
Ivan Kaygorodov • Salvatore Siciliano • Mykola Khrypсhenko • Jobir Adashev