On the matched product of set-theoretical solutions

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March 20, 2019
11.00 – 13.00 – M5
Paola Stefanelli

The problem of finding set-theoretical solutions of the Yang-Baxter equation [2] (shortly solutions) has been dealt with from different points of view in the last years.
In [1] a novel construction technique for solutions was developed, the matched product. In this talk, we will display a method to construct new classes of particular solutions through the matched product of other solutions in the same class. As a particular case, starting from involutive (resp. idempotent) solutions the matched product is still involutive (resp. idempotent), and vice versa.

[1] F. Catino, I. Colazzo, P. Stefanelli, The matched product of set-theoretical solutions of the Yang-Baxter equation, submitted.
[2] V.G. Drinfeld, On some unsolved problems in quantum group theory. Lecture Notes in Math. 1510 (1992) 1-8.