  We show that a nondegenerate unitary solution $r(u,v)$ of the associative
Yang-Baxter equation (AYBE) for $\Mat(N,\C)$ (see math.AG/0008156) with the
Laurent series at $u=0$ of the form $r(u,v)=\frac{1\ot 1}{u}+r_0(v)+...$
satisfies the quantum Yang-Baxter equation, provided the projection of $r_0(v)$
to traceless matrices has a period. We classify all such solutions of the AYBE
extending the work of Schedler math.QA/0212258. We also characterize solutions
coming from triple Massey products in the derived category of coherent sheaves
on cycles of projective lines.
