Speaker: Andrei Zotov (Steklov Mathematical Institute RAS, ITMP MSU)

Title: Applications of associative Yang-Baxter equation for constructing integrable systems

Date and time:  28.01.2026, 17:00 (GMT +03:00)

Abstract: We review different applications of the associative Yang-Baxter equation (AYBE) to integrable systems. Namely, we study a class of quantum R-matrices in the fundamental representation which satisfy not only the standard quantum Yang-Baxter equation but also the quadratic relation called AYBE. It allows to propose constructions of the classical Lax pairs for integrable tops, quadratic r-matrix structures of Sklyanin type, classical spin chains and continuous 1+1 integrable field theories of Landau-Lifshitz type. One of the most general is the model of interacting tops. Another construction is an R-matrix valued Lax pair. With its help one can define a quantization for the model of interacting tops. By proceeding to half-quantum (hybrid) Lax equations we obtain a family of quantum long-range spin chains of the Haldane-Shastry type. Finally, we briefly discuss extension of the AYBE to BC_N root system, which involves the boundary K-matrices.

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