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

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

Deadline for manuscript submissions: closed (1 July 2012)

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: http://www.imar.ro/organization/people/PRS/PRS_118.php?PAG=PRS
E-Mail: florin.nichita@imar.ro
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 theoretical physics, in a paper (1968) by the Nobel laureate C.N. Yang, and in statistical mechanics, in R.J. Baxter's work (1971). 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 (quasi-triangular Hopf algebras, Yetter-Drinfeld categories, Lie (super)algebras, algebra structures, Boolean algebras, 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 equations, the related algebraic structures, and their applications are invited. We would like to gather together both relevant reviews (with historical notes, open problems or research directions) and research papers (on the new developments of the Yang-Baxter equations).

Dr. Florin Felix Nichita
Guest Editor

Keywords

  • Yang-Baxter equation
  • Yang-Baxter system
  • Quantum Groups
  • Hopf algebra
  • braid group
  • braided category

Published Papers (11 papers)

Axioms 2012, 1(3), 324-364; doi:10.3390/axioms1030324
Received: 2 July 2012; in revised form: 23 August 2012 / Accepted: 29 September 2012 / Published: 23 October 2012
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Communication: The Hecke Bicategory
Axioms 2012, 1(3), 291-323; doi:10.3390/axioms1030291
Received: 19 July 2012; in revised form: 4 September 2012 / Accepted: 5 September 2012 / Published: 9 October 2012
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Axioms 2012, 1(3), 259-290; doi:10.3390/axioms1030259
Received: 2 July 2012; in revised form: 17 September 2012 / Accepted: 17 September 2012 / Published: 5 October 2012
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Axioms 2012, 1(2), 226-237; doi:10.3390/axioms1020226
Received: 28 June 2012; in revised form: 13 August 2012 / Accepted: 4 September 2012 / Published: 20 September 2012
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Axioms 2012, 1(2), 201-225; doi:10.3390/axioms1020201
Received: 10 July 2012; in revised form: 21 August 2012 / Accepted: 23 August 2012 / Published: 17 September 2012
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Axioms 2012, 1(2), 186-200; doi:10.3390/axioms1020186
Received: 2 July 2012; in revised form: 7 August 2012 / Accepted: 16 August 2012 / Published: 27 August 2012
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Axioms 2012, 1(2), 173-185; doi:10.3390/axioms1020173
Received: 29 June 2012; in revised form: 24 July 2012 / Accepted: 30 July 2012 / Published: 10 August 2012
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Axioms 2012, 1(2), 155-172; doi:10.3390/axioms1020155
Received: 20 June 2012; in revised form: 15 July 2012 / Accepted: 17 July 2012 / Published: 24 July 2012
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Axioms 2012, 1(2), 149-154; doi:10.3390/axioms1020149
Received: 4 May 2012; in revised form: 25 June 2012 / Accepted: 25 June 2012 / Published: 16 July 2012
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Axioms 2012, 1(2), 111-148; doi:10.3390/axioms1020111
Received: 13 February 2012; in revised form: 20 June 2012 / Accepted: 20 June 2012 / Published: 4 July 2012
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Axioms 2012, 1(1), 74-98; doi:10.3390/axioms1010074
Received: 9 April 2012; in revised form: 4 June 2012 / Accepted: 4 June 2012 / Published: 15 June 2012
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Last update: 25 February 2014

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