Special Issue "Hopf Algebras, Quantum Groups and Yang-Baxter Equations 2013"

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

Deadline for manuscript submissions: closed (15 August 2013)

Special Issue Editor

Guest Editor
Dr. Florin Felix Nichita

Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania
Website | E-Mail
Phone: + 40 244 598 194
Interests: (co)algebras; bialgebras; Yang-Baxter equations; Lie (co)algebras; quantum groups; Hopf algebras; duality theories

Special Issue Information

Dear Colleagues,

The Yang-Baxter equation first appeared in a paper by the Nobel laureate C.N. Yang and in R.J. Baxter's work. At the Kyoto International Mathematics Congress (1990), three of the four Fields Medalists were awarded prizes for their work related to the Yang-Baxter equation.

This equation plays a crucial role in many areas of mathematics, physics, and computer science. Many scientists have used the axioms of various algebraic structures or computer calculations in order to produce solutions for it, but the full classification of its solutions remains an open problem.

As we continue the scientific directions of our previous special issue on various aspects of the Yang-Baxter equations and the related structures, we would like to gather together both interesting reviews and research papers.

Dr. Florin Felix Nichita
Guest Editor

Submission

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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Keywords

  • Yang-Baxter equations
  • (Quasi-triangular) Hopf algebras
  • Quantum Groups
  • FRT constructions
  • knot invariants
  • Yang-Baxter systems
  • braided categories
  • braid groups
  • entwining structures
  • braided algebras

Related Special Issue

Published Papers (2 papers)

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Research

Open AccessArticle R-Matrices, Yetter-Drinfel'd Modules and Yang-Baxter Equation
Axioms 2013, 2(3), 443-476; doi:10.3390/axioms2030443
Received: 14 August 2013 / Revised: 28 August 2013 / Accepted: 30 August 2013 / Published: 5 September 2013
Cited by 3 | PDF Full-text (402 KB)
Abstract
In the first part we recall two famous sources of solutions to the Yang-Baxter equation—R-matrices and Yetter-Drinfel0d (=YD) modules—and an interpretation of the former as a particular case of the latter. We show that this result holds true in the more general case
[...] Read more.
In the first part we recall two famous sources of solutions to the Yang-Baxter equation—R-matrices and Yetter-Drinfel0d (=YD) modules—and an interpretation of the former as a particular case of the latter. We show that this result holds true in the more general case of weak R-matrices, introduced here. In the second part we continue exploring the “braided” aspects of YD module structure, exhibiting a braided system encoding all the axioms from the definition of YD modules. The functoriality and several generalizations of this construction are studied using the original machinery of YD systems. As consequences, we get a conceptual interpretation of the tensor product structures for YD modules, and a generalization of the deformation cohomology of YD modules. This homology theory is thus included into the unifying framework of braided homologies, which contains among others Hochschild, Chevalley-Eilenberg, Gerstenhaber-Schack and quandle homologies. Full article
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations 2013)
Open AccessCommunication Yang-Baxter Systems, Algebra Factorizations and Braided Categories
Axioms 2013, 2(3), 437-442; doi:10.3390/axioms2030437
Received: 13 August 2013 / Revised: 30 August 2013 / Accepted: 30 August 2013 / Published: 3 September 2013
Cited by 3 | PDF Full-text (143 KB) | HTML Full-text | XML Full-text
Abstract
The Yang-Baxter equation first appeared in a paper by the Nobel laureate, C.N. Yang, and in R.J. Baxter’s work. Later, Vladimir Drinfeld, Vaughan F. R. Jones and Edward Witten were awarded Fields Medals for their work related to the Yang-Baxter equation. After a
[...] Read more.
The Yang-Baxter equation first appeared in a paper by the Nobel laureate, C.N. Yang, and in R.J. Baxter’s work. Later, Vladimir Drinfeld, Vaughan F. R. Jones and Edward Witten were awarded Fields Medals for their work related to the Yang-Baxter equation. After a short review on this equation and the Yang-Baxter systems, we consider the problem of constructing algebra factorizations from Yang-Baxter systems. Our sketch of proof uses braided categories. Other problems are also proposed. Full article
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations 2013)

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