Séminaires : Séminaire d'Algèbre

Equipe(s) : gr,
Responsables :J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
Email des responsables : Jacques Alev <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : 001
Adresse :IHP


Orateur(s) Natalia IYUDU - Edimbourg,
Titre The proof of the Kontsevich conjecture on noncommutative birational transformations
Horaire14:00 à 15:00
RésumeI will talk about our recent proof (arXiv1305.1965) of the Kontsevich conjecture dated back at 1996, and mentioned at the 2011 Arbeitstagung talk on 'Noncommutative identities' (arXiv1109.2469). This conjecture says that certain transformations given by matrices over free noncommutative algebra with inverses are periodic, on the level of orbits of the left/right diagonal action. Namely, let $M_{ij}, 1\leq i,j \leq 3$ be a matrix, whose entries are independent noncommutative variables. Let us consider three birational involutions: $\quad I_1: M \to M^{-1}\quad$ $I_2: M_{ij} \to (M_{ij})^{-1}, \forall i,j \quad$ $I_3: M \to M^t\quad$ Then the composition $\Phi=I_1 \circ I_2 \circ I_3 $ has order three.