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 equation is discussed as well. It acquires additional term in the case of supersymmetric R -matrices.

中文翻译：

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椭圆R-矩阵的奇奇超对称化

我们研究Kronecker椭圆函数的奇数超对称版本的一般ansatz，它满足一个Fay身份。所得结果用于构造经典和量子椭圆R矩阵的奇数超对称类似物。显示它们满足经典的Yang–Baxter方程和相关的Yang–Baxter方程。讨论了杨-巴克斯特量子方程。在超对称R矩阵的情况下，它获得了附加项。