Research output: Contribution to journal › Article

**Associative Yang-Baxter equation and Fukaya categories of square-tiled surfaces.** / Lekili, Yanki; Polishchuk, Alexander.

Research output: Contribution to journal › Article

Lekili, Y & Polishchuk, A 2019, 'Associative Yang-Baxter equation and Fukaya categories of square-tiled surfaces', *ADVANCES IN MATHEMATICS*, vol. 343, pp. 273-315. https://doi.org/10.1016/j.aim.2018.11.018

Lekili, Y., & Polishchuk, A. (2019). Associative Yang-Baxter equation and Fukaya categories of square-tiled surfaces. *ADVANCES IN MATHEMATICS*, *343*, 273-315. https://doi.org/10.1016/j.aim.2018.11.018

Lekili Y, Polishchuk A. Associative Yang-Baxter equation and Fukaya categories of square-tiled surfaces. ADVANCES IN MATHEMATICS. 2019 Feb 5;343:273-315. https://doi.org/10.1016/j.aim.2018.11.018

@article{61fbe103225e458ca364ddb74c4fa595,

title = "Associative Yang-Baxter equation and Fukaya categories of square-tiled surfaces",

abstract = "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.",

keywords = "Associative Yang–Baxter equation, Fukaya category, Square-tiled surface",

author = "Yanki Lekili and Alexander Polishchuk",

year = "2019",

month = feb,

day = "5",

doi = "https://doi.org/10.1016/j.aim.2018.11.018",

language = "English",

volume = "343",

pages = "273--315",

journal = "ADVANCES IN MATHEMATICS",

issn = "0001-8708",

publisher = "ACADEMIC PRESS INC",

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TY - JOUR

T1 - Associative Yang-Baxter equation and Fukaya categories of square-tiled surfaces

AU - Lekili, Yanki

AU - Polishchuk, Alexander

PY - 2019/2/5

Y1 - 2019/2/5

N2 - 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.

AB - 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.

KW - Associative Yang–Baxter equation

KW - Fukaya category

KW - Square-tiled surface

UR - http://www.scopus.com/inward/record.url?scp=85057417612&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.aim.2018.11.018

DO - https://doi.org/10.1016/j.aim.2018.11.018

M3 - Article

VL - 343

SP - 273

EP - 315

JO - ADVANCES IN MATHEMATICS

JF - ADVANCES IN MATHEMATICS

SN - 0001-8708

ER -

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