Speaker:  Valeriy Bardakov (Sobolev Institute of Mathematics, Novosibirsk, Russia)

Date and time:  13.10.2021, 17:00 (GMT +03:00)

Title: n-simplex equation and corresponding algebraic systems

Abstract:  

n-simplex equation (shortly n-SE) is a generalization of the Yang-Baxter equation, which is 2-simplex equation. In this talk I give a way to write n-simplex equation for arbitrary n, give its geometric interpretation, introduce operation tropicalization which give a possibility to construct piecewise linear solutions of n-SE from some rational solutions. Further, I discuss a construction of solution of n-SE on group extensions, introduce verbal solutions and formulate a theorem of existence of elementary solutions of 4-SE on arbitrary group. At the end, I introduce some algebraic systems with ternary algebraic operations related with 3-simplex equation.

This is joint work with B. Chuzinov, I. Emel'yanenko, M. Ivanov, T. Kozlovskaya, and V. Leshkov.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com