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We show that a nondegenerate unitary solution r(u, v) of the associative Yang–Baxter equation (AYBE) for  Mat(N,C)\mathrm{Mat}(N,\mathcal{C}) (see [7]) with the Laurent series at u = 0 of the form r(u, v) =  \frac1 Ä</font>1u\frac{1 \otimes 1}{u} + r 0(v) + ⋯ satisfies the quantum Yang–Baxter equation, provided the projection of r 0(v) to sl N  ⊗ sl N  has a period. We classify all such solutions of the AYBE, extending the work of Schedler [8]. We also characterize solutions coming from triple Massey products in the derived category of coherent sheaves on cycles of projective lines.

Massey Products on Cycles of Projective Lines and Trigonometric Solutions of the Yang–Baxter Equations