Conference abstracts

Session S12 - Group Theory

July 29, 16:00 ~ 16:25

## On set-theoretic solutions to the Yang-Baxter equation

### University of Nantes, France   -   lebed.victoria@gmail.com

Since the seminal work of Drinfel'd, the study of set-theoretic solutions to the Yang-Baxter equation (with we will simply call solutions) has always remained a dynamic research area. To any solution, one can associate a group, which opens the way for applying group-theoretic tools to the study of the YBE. This construction is classical and well explored. In this talk, to any solution we will associate another type of structure, called a shelf. This is a set with a binary operation $*$ satisfying the self-distributivity relation $(a*b)*c=(a*c)*(b*c)$. The associated shelf captures many properties of the original solution, and in particular contains information about its associated group. Thus to understand the group-theoretic aspects of solutions, it is instructive to look at their shelves, which are much easier to deal with. These ideas are also fruitful in the study of the (co)homology of solutions.

Joint work with Leandro Vendramin (Universidad de Buenos Aires, Argentina).