Cohomology and extensions of braces (Q305143)

The paper continues previous work of the authors on homology of set-theoretic solutions of the Yang-Baxter equation [Adv. Math. 304, 1219--1261 (2017; Zbl 1356.16027)]. It is shown there, in particular, that central extensions of cycle sets are classified by the second cohomology group. As cycle sets correspond to a class of solutions, this leads to constructions of new solutions and contributes to a refined understanding of their structure. In the paper under review, these methods are further developed in the framework of linear cycle sets which are known to be equivalent to braces.