# Distributive biracks and solutions of the Yang-Baxter equation

## TL;DR

This paper explores a new class of solutions to the Yang-Baxter equation called distributive biracks, demonstrating their properties and the nilpotency of their associated groups, thus broadening understanding of algebraic structures related to the equation.

## Contribution

It introduces distributive biracks as a generalization of self-distributive solutions and analyzes their properties, including the nilpotency of their Yang-Baxter groups.

## Key findings

- Yang-Baxter groups of these solutions are nilpotent
- Distributive biracks generalize self-distributive solutions
- Results are formulated using the language of biracks

## Abstract

We investigate a class of non-involutive solutions of the Yang-Baxter equation which generalize self-distributive (derived) solutions. In particular, we study generalized multipermutation solutions in this class. We show that the Yang-Baxter (permutation) groups of such solutions are nilpotent. We formulate the results in the language of biracks.