TY - GEN AU - Florin Felix Nichita (Ed) TI - Hopf Algebras, Quantum Groups and Yang-Baxter Equations SN - books978-3-03897-325-6 PY - 2019/// PB - MDPI - Multidisciplinary Digital Publishing Institute KW - braided category KW - quasitriangular structure KW - quantum projective space KW - Hopf algebra KW - quantum integrability KW - duality KW - six-vertex model KW - Quantum Group KW - Yang-Baxter equation KW - star-triangle relation KW - R-matrix KW - Lie algebra KW - bundle KW - braid group N1 - Open Access N2 - 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 UR - https://www.mdpi.com/books/pdfview/book/1119 UR - https://directory.doabooks.org/handle/20.500.12854/49556 ER -