This article is cited in 2 papers

Belousov's theorem and the quantum Yang–Baxter equation

Jonathan D. H. Smith

Dept. of Math., Iowa State Univ., Ames, IA 50011, U.S.A.

Abstract: 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.

Keywords and phrases: Belousov theorem, quasigroup, loop, quantum Yang–Baxter equation, quantum quasigroup, distributive, isotopy.

MSC: 20N05, 16T25

Received: 23.08.2015

Language: English