Geodesic
Non-commutative differential geometry related to the Yang--Baxter equation
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 11, Tome 199 (1992), pp. 51-70

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An analogue of the differential calculus associated with a unitary solution of quantum Yang–Baxter equation is constructed. An example of a ring sheaf is given in which local solutions of the quantum Yang–Baxter equation exist but not global ones. 
@article{ZNSL_1992_199_a4,
     author = {D. Gurevich and A. Radul and V. Rubzov},
     title = {Non-commutative differential geometry related to the {Yang--Baxter} equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {51--70},
     publisher = {mathdoc},
     volume = {199},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_199_a4/}
}
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D. Gurevich; A. Radul; V. Rubzov. Non-commutative differential geometry related to the Yang--Baxter equation. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 11, Tome 199 (1992), pp. 51-70. http://geodesic.mathdoc.fr/item/ZNSL_1992_199_a4/