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Axioms
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Hopf Algebras, Quantum Groups and Yang-Baxter Equations 2013
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Hopf Algebras, Quantum Groups and Yang-Baxter Equations 2013

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

Deadline for manuscript submissions: closed (15 August 2013) | Viewed by 10562

Special Issue Editor

Dr. Florin Felix Nichita

E-Mail Website
Guest Editor
Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania
Interests: (co)algebras; bialgebras; Yang–Baxter equations; Lie (co)algebras; quantum groups; Hopf algebras; duality theories
Special Issues, Collections and Topics in MDPI journals

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

Manuscript Submission Information

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. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short 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.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


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

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Published Papers (2 papers)

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Research

402 KiB  
Article
R-Matrices, Yetter-Drinfel'd Modules and Yang-Baxter Equation
by Victoria Lebed
Axioms 2013, 2(3), 443-476; https://doi.org/10.3390/axioms2030443 - 05 Sep 2013
Cited by 4 | Viewed by 5764
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)
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143 KiB  
Communication
Yang-Baxter Systems, Algebra Factorizations and Braided Categories
by Florin F. Nichita
Axioms 2013, 2(3), 437-442; https://doi.org/10.3390/axioms2030437 - 03 Sep 2013
Cited by 5 | Viewed by 4266
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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