Odd supersymmetrization of elliptic R-matrices

TL;DR

This paper develops an odd supersymmetric extension of elliptic R-matrices, satisfying key integrability equations, and explores their classical and quantum properties, advancing the understanding of supersymmetric integrable systems.

Contribution

It introduces a novel odd supersymmetric version of elliptic R-matrices that satisfy classical and quantum Yang-Baxter equations, extending the mathematical framework of integrable models.

Findings

Supersymmetric elliptic R-matrices satisfy the classical Yang-Baxter equation.

They also satisfy the associative Yang-Baxter equation.

Quantum Yang-Baxter equation is modified with additional terms in the supersymmetric case.

Abstract

We study a general ansatz for an odd supersymmetric version of the Kronecker elliptic function, which satisfies the genus one Fay identity. The obtained result is used for construction of the odd supersymmetric analogue for the classical and quantum elliptic $R$-matrices. They are shown to satisfy the classical Yang-Baxter equation and the associative Yang-Baxter equation. The quantum Yang-Baxter is discussed as well. It acquires additional term in the case of supersymmetric $R$-matrices.