Reprint

Hopf Algebras, Quantum Groups and Yang-Baxter Equations

Edited by
January 2019
238 pages
  • ISBN978-3-03897-324-9 (Paperback)
  • ISBN978-3-03897-325-6 (PDF)

This is a Reprint of the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations that was published in

Computer Science & Mathematics
Physical Sciences
Summary
The Yang-Baxter equation first appeared in theoretical physics, in a paper by the Nobel laureate C.N. Yang and in the work of R.J. Baxter in the field of Statistical Mechanics. At the 1990 International Mathematics Congress, Vladimir Drinfeld, Vaughan F. R. Jones, and Edward Witten were awarded Fields Medals for their work related to the Yang-Baxter equation. It turned out that this equation is one of the basic equations in mathematical physics; more precisely, it is used for introducing the theory of quantum groups. It also plays a crucial role in: knot theory, braided categories, the analysis of integrable systems, 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, quandles, group actions, Lie (super)algebras, brace structures, (co)algebra structures, Jordan triples, Boolean algebras, relations on sets, etc.) or computer calculations (and Grobner bases) in order to produce solutions for the Yang-Baxter equation. However, the full classification of its solutions remains an open problem. At present, the study of solutions of the Yang-Baxter equation attracts the attention of a broad circle of scientists. The current volume highlights various aspects of the Yang-Baxter equation, related algebraic structures, and applications.
Format
  • Paperback
License and Copyright
© 2019 by the authors; CC BY-NC-ND license
Keywords
paraparticles; relative paraparticle sets; universal enveloping algebras; Lie (super)algebras; -colored -graded Lie algebras; braided groups; graded Hopf algebras; braided (graded) modules; braided (graded) tensor products; braided and symmetric monoidal categories; quasitriangularity; R-matrix; bicharacter; color function; commutation factor; quiver; species; lie algebra; representation theory; root system; valued graph; modulated quiver; tensor algebra; path algebra; Ringel–Hall algebra; non-commutative symmetric functions; Hasse-Schmidt derivation; higher derivation; Heerema formula; Mirzavaziri formula; non-commutative Newton formulas; algebra; coalgebra; bialgebra; Myhill–Nerode theorem; Myhill–Nerode bialgebra; quasitriangular structure; corings; ring extension; duality; Yang–Baxter equation; vertex model; bialgebra; coalgebra; Bethe ansatz; quantum real weighted projective space; principal comodule algebra; noncommutative line bundle; Hopf algebra; Drinfel’d double construction; quantum integrability; Yang–Baxter equation; Hopf algebra; weights; grouplike; skew-primitive; Hecke algebras; categorification; groupoidification; Yang–Baxter equations; Zamalodchikov tetrahedron equations; spans; enriched bicategories; buildings; incidence geometries; Frobenius–Schur indicator; category with duality; Hopf algebra; quantum groups

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