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Quantum Quasigroups and the Quantum Yang–Baxter Equation

Department of Mathematics, Iowa State University, Ames, IA 50011, USA
Academic Editor: Florin Felix Nichita
Axioms 2016, 5(4), 25;
Received: 11 October 2016 / Revised: 30 October 2016 / Accepted: 1 November 2016 / Published: 9 November 2016
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations 2016)
PDF [278 KB, uploaded 9 November 2016]


Quantum quasigroups are algebraic structures providing a general self-dual framework for the nonassociative extension of Hopf algebra techniques. They also have one-sided analogues, which are not self-dual. The paper presents a survey of recent work on these structures, showing how they furnish various solutions to the quantum Yang–Baxter equation. View Full-Text
Keywords: Hopf algebra; quantum group; quasigroup; Moufang loop; quantum Yang–Baxter equation Hopf algebra; quantum group; quasigroup; Moufang loop; quantum Yang–Baxter equation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Smith, J. Quantum Quasigroups and the Quantum Yang–Baxter Equation. Axioms 2016, 5, 25.

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