Research output: Contribution to journal › Article

Yanki Lekili, Alexander Polishchuk

Original language | English |
---|---|

Pages (from-to) | 273-315 |

Number of pages | 43 |

Journal | ADVANCES IN MATHEMATICS |

Volume | 343 |

Early online date | 30 Nov 2018 |

DOIs | |

Accepted/In press | 20 Jul 2018 |

E-pub ahead of print | 30 Nov 2018 |

Published | 5 Feb 2019 |

Additional links |

**Associative Yang-Baxter equation_LEKILI_Accepted20July2018_GREEN AAM (CC BY-NC-ND)**yangbaxter.pdf, 379 KB, application/pdf

Uploaded date:16 Oct 2018

Version:Accepted author manuscript

We show that all strongly non-degenerate trigonometric solutions of the associative Yang–Baxter equation (AYBE) can be obtained from triple Massey products in the Fukaya categories of square-tiled surfaces. Along the way, we give a classification result for cyclic -algebra structures on a certain Frobenius algebra associated with a pair of 1-spherical objects in terms of the equivalence classes of the corresponding solutions of the AYBE. As an application, combining our results with homological mirror symmetry for punctured tori (cf. [17]), we prove that any two simple vector bundles on a cycle of projective lines are related by a sequence of 1-spherical twists and their inverses.

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