Session S16 - Quantum symmetries

Monday, July 19, 19:20 ~ 19:45 UTC-3

Multipermutation solutions to the Yang-Baxter equation

Emiliano Acri

IMAS-UBA, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this work, we study the structure group of a certain important class of solutions to the Yang-Baxter equation, the so-called multipermutation solutions. The structure group of one of these solutions admits a left order. We explore the relation between this class of solutions and groups with the unique product property. We also provide an algorithm that allows us to check if a group has not this property, at least for low order solutions. We develop a notion of nilpotency for skew braces in order to generalize the study of multipermutation solutions.

Joint work with R. Lutowski (Gdańsk, Poland) and L. Vendramin (IMAS-UBA, Argentina).

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