Massey products on cycles of projective lines and trigonometric solutions of the Yang-Baxter equations

Details Massey products on cycles of projective lines and trigonometric solutions of the Yang-Baxter equations Massey products on cycles of projective lines and trigonometric solutions of the Yang-Baxter equations

2006-12-27

arxiv.org/abs/math/0612761v4

Mathematics

Quantum Algebra

32 pages, v3: added the proof of the fact that all nondegenerate unitary solutions of the AYBE depending only on spectral para

Scientific paper

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.

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