LEADER 03109nam 22005653a 450 001 9910346679403321 005 20250203235431.0 010 $a9783038973256 010 $a3038973254 024 8 $a10.3390/books978-3-03897-325-6 035 $a(CKB)4920000000094873 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/49556 035 $a(ScCtBLL)7c55e0da-8057-458b-a9c1-c3c2617123a0 035 $a(OCoLC)1163815771 035 $a(oapen)doab49556 035 $a(EXLCZ)994920000000094873 100 $a20250203i20192019 uu 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aHopf Algebras, Quantum Groups and Yang-Baxter Equations$fFlorin Felix Nichita 210 $cMDPI - Multidisciplinary Digital Publishing Institute$d2019 210 1$aBasel, Switzerland :$cMDPI,$d2019. 215 $a1 electronic resource (238 p.) 311 08$a9783038973249 311 08$a3038973246 330 $aThe 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. 610 $abraided category 610 $aquasitriangular structure 610 $aquantum projective space 610 $aHopf algebra 610 $aquantum integrability 610 $aduality 610 $asix-vertex model 610 $aQuantum Group 610 $aYang-Baxter equation 610 $astar-triangle relation 610 $aR-matrix 610 $aLie algebra 610 $abundle 610 $abraid group 700 $aNichita$b Florin Felix$01327012 801 0$bScCtBLL 801 1$bScCtBLL 906 $aBOOK 912 $a9910346679403321 996 $aHopf Algebras, Quantum Groups and Yang-Baxter Equations$94319589 997 $aUNINA