On elliptic solutions of the associative Yang-Baxter equation

TL;DR

This paper proves that elliptic solutions to the associative Yang-Baxter equation originate from specific spherical orders on elliptic curves, providing a direct and conceptual understanding of their origin.

Contribution

It establishes a direct link between elliptic solutions of the associative Yang-Baxter equation and spherical orders on elliptic curves, clarifying their geometric origin.

Findings

Elliptic solutions are derived from spherical orders.

Provides a direct proof of the connection.

Enhances understanding of the geometric structure behind solutions.

Abstract

We give a direct proof of the fact that elliptic solutions of the associative Yang-Baxter equation arise from appropriate spherical orders on an elliptic curve.