Special Issue "Hopf Algebras, Quantum Groups and YangBaxter Equations"
A special issue of Axioms (ISSN 20751680).
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 1764, 014700 Bucharest, Romania
Website: http://www.imar.ro/organization/people/PRS/PRS_118.php?PAG=PRS
EMail: florin.nichita@imar.ro
Interests: (co)algebras; bialgebras; YangBaxter equations; Lie (co)algebras; quantum groups; Hopf algebras; duality theories
Special Issue Information
Dear Colleagues,
The YangBaxter 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, noncommutative descent theory, quantum computing, noncommutative geometry, etc.
Many scientists have used the axioms of various algebraic structures (quasitriangular Hopf algebras, YetterDrinfeld categories, Lie (super)algebras, algebra structures, Boolean algebras, etc) or computer calculations in order to produce solutions for the YangBaxter equation. However, the full classification of its solutions remains an open problem.
Contributions related to the various aspects of the YangBaxter 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 YangBaxter equations).
Dr. Florin Felix Nichita
Guest Editor
Keywords
 YangBaxter equation
 YangBaxter system
 Quantum Groups
 Hopf algebra
 braid group
 braided category
Published Papers (11 papers)
Axioms 2012, 1(3), 324364; 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), 291323; 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), 259290; 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), 226237; 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), 201225; 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), 186200; 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), 173185; 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), 155172; 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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Communication:
HasseSchmidt Derivations and the Hopf Algebra of NonCommutative Symmetric Functions
Axioms 2012, 1(2), 149154; 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), 111148; 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), 7498; 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