Majid, Shahn Quasitriangular Hopf algebras and Yang-Baxter equations. (English) Zbl 0709.17009 Int. J. Mod. Phys. A 5, No. 1, 1-91 (1990). Summary: This expository article is intended as an informal introduction to the theory of quasitriangular Hopf algebras and its connections with physics. Basic properties and applications of Hopf algebras and Yang-Baxter equations are reviewed, with the quantum group \(U_ q(sl_ 2)\) as a frequent example. The development builds up to the representation theory of quasitriangular Hopf algebras. Much of the abstract representation theory is new, including a formula for the rank of a representation. Cited in 4 ReviewsCited in 159 Documents MSC: 17B37 Quantum groups (quantized enveloping algebras) and related deformations 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 16G99 Representation theory of associative rings and algebras 22E70 Applications of Lie groups to the sciences; explicit representations 57T05 Hopf algebras (aspects of homology and homotopy of topological groups) 81-02 Research exposition (monographs, survey articles) pertaining to quantum theory Keywords:quantization of Lie bialgebras; Hopf algebra duality; quantum mechanics; quasitriangular Hopf algebras; Yang-Baxter equations; quantum group; representation; rank PDFBibTeX XMLCite \textit{S. Majid}, Int. J. Mod. Phys. A 5, No. 1, 1--91 (1990; Zbl 0709.17009) Full Text: DOI