# Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation - Mathematics > Algebraic Geometry

Abstract: In this paper we study unitary solutions of the associative Yang-Baxterequation AYBE with spectral parameters. We show that to each point $\tau$from the upper half-plane and an invertible $n \times n$ matrix $B$ withcomplex coefficients one can attach a solution of AYBE with values in $Mat {n\times n}\CC \otimes Mat {n \times n}\CC$, depending holomorphically on$\tau$ and $B$. Moreover, we compute some of these solutions explicitly.

Author: Igor Burban, Thilo Henrich

Source: https://arxiv.org/