Belousov's theorem and the quantum Yang–Baxter equation

Quantum quasigroups are self-dual objects that provide a general framework for the nonassociative extension of quantum group techniques. Within this context, the classical theorem of Belousov on the isotopy of distributive quasigroups and commutative Moufang loops is reinterpreted to yield solutions of the quantum Yang–Baxter equation. A new concept of principal bimagma isotopy is introduced.