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Axioms 2015, 4(4), 423-435; doi:10.3390/axioms4040423

Yang–Baxter Equations, Computational Methods and Applications

Simion Stoilow Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania
Academic Editor: Angel Garrido
Received: 31 August 2015 / Revised: 28 September 2015 / Accepted: 28 September 2015 / Published: 9 October 2015
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations 2015)
View Full-Text   |   Download PDF [201 KB, uploaded 9 October 2015]

Abstract

Computational methods are an important tool for solving the Yang–Baxter equations (in small dimensions), for classifying (unifying) structures and for solving related problems. This paper is an account of some of the latest developments on the Yang–Baxter equation, its set-theoretical version and its applications. We construct new set-theoretical solutions for the Yang–Baxter equation. Unification theories and other results are proposed or proven. View Full-Text
Keywords: Yang–Baxter equation; computational methods; universal gate; non-associative structures; associative algebras; Jordan algebras; Lie algebras Yang–Baxter equation; computational methods; universal gate; non-associative structures; associative algebras; Jordan algebras; Lie algebras
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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Nichita, F.F. Yang–Baxter Equations, Computational Methods and Applications. Axioms 2015, 4, 423-435.

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