Hopf Algebras, Quantum Groups and Yang-Baxter Equations 2015

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (31 January 2016) | Viewed by 4563

Special Issue Editor

Special Issue Information

Dear Colleagues,

The Yang-Baxter Equation first appeared in theoretical physics, in a paper of the Nobel laureate C.N. Yang, and in statistical mechanics, in R.J. Baxter's work. Later, it turned out that this equation plays a crucial role in: quantum groups, knot theory, braided categories, analysis of integrable systems, quantum mechanics, non-commutative descent theory, quantum computing, non-commutative geometry, etc.

Many scientists have used the axioms of various algebraic structures (quasitriangular Hopf algebras, Yetter-Drinfeld categories, Lie (super)algebras, algebra structures, Boolean algebras, brace structures, relations on sets, etc.) or computer calculations in order to produce solutions for the Yang-Baxter Equation. However, the full classification of its solutions remains an open problem.

Contributions related to the various aspects of the Yang-Baxter Equation, the related algebraic structures, and their applications are invited. We would like to gather together relevant reviews, research articles, and communications.

Dr. Florin Felix Nichita
Guest Editor

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Keywords

  • Yang-Baxter equation
  • quantum groups
  • link invariants
  • virtual knot theory
  • set-theoretical Yang-Baxter equation
  • brace structure
  • quasitriangular Hopf algebra
  • braid group
  • braided category
  • classical Yang-Baxter equation
  • Myhill-Nerode monoid
  • Yang-Baxter system

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Article
Yang–Baxter Equations, Computational Methods and Applications
by Florin F. Nichita
Axioms 2015, 4(4), 423-435; https://doi.org/10.3390/axioms4040423 - 09 Oct 2015
Cited by 14 | Viewed by 4169
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations 2015)
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