The invention of quantum groups is one of the outstanding achievements of mathematical physics and mathematics in the late twentieth century. The birth of the new theory and its rapid development are results of a strong interrelation between mathematics and physics. Quantu~ groups arose in the work of L.D. Faddeev and the Leningrad school on the inverse scattering method in order to solve integrable models. The algebra Uq(sh) appeared first in 1981 in a paper by P.P. Kulish and N.Yu. Reshetikhin on the study of integrable XYZ models with highest spin. Its Hopf algebra structure was discovered later by E.K. Sklyanin. A major event was the discovery by V.G. Drinfeld and M. Jimbo around 1985 of a class of Hopf algebras which can be considered as one-parameter deforma- tions of universal enveloping algebras of semisimple complex Lie algebras. These Hopf algebras will be called Drinfeld-Jimbo algebras in this book. Al- most simultaneously, S.L. Woronowicz invented the quantum group SUq(2) and developed his theory of compact quantum matrix groups. An algebraic approach to quantized coordinate algebras was given about this time by Yu.I. Manin.
- ISBN13 9783642646010
- Publish Date 14 December 2011 (first published 11 December 1997)
- Publish Status Active
- Publish Country DE
- Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Edition Softcover reprint of the original 1st ed. 1997
- Format Paperback
- Pages 552
- Language English