Odd supersymmetrization of elliptic R-matrices

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.To the 80-th anniversary of Andrei Slavnov

On elliptic solutions of the associative Yang-Baxter equation

“…where D ⊂ P × P is the locus defined by (8) and Ξ ⊂ Ȇ × Ȇ is the diagonal. Let X := B × E. Then the canonical projection X π − B admits two canonical sections…”