Construction of quantum doubles from solutions of Yang-Baxter system

The construction of quantum doubles based on the results of Vladimirov's article (Mod. Phys. Lett. A 8 (1993) 1315) was considered. A.A. Vladimirov claimed that to every triple of invertible matrices satisfying certain Yang-Baxter-like system should be possible to associate a quantum double. The most interesting conclusion of the current research is that the corresponding quantum double is completely determined by one matrix of the triple, the other matrices are irrelevant. Several examples of quantum doubles were obtained.