Introduction to Quantum Groups and Crystal Bases

ISBN-13: 9780821828748 / Angielski / Twarda / 2002 / 328 str.

Jin Hong; Korea) Seoul Kang Hong (Korea Institute For Advanced Study

Opis

The notion of a quantum group was introduced by V.G. Dinfeld and M. Jimbo, independently, in their study of the quantum Yang-Baxter equation arising from 2-dimensional solvable lattice models. Quantum groups are certain families of Hopf algebras that are deformations of universal enveloping algebras of Kac-Moody algebras. And over the last 20 years of the 20th century, they have turned out to be the fundamental algebraic structure behind many branches of mathematics and mathematical physics, such as solvable lattice models in statistical mechanics, topological invariant theory of links and knots, representation theory of Kac-Moody algebras, representation theory of algebraic structures, topological quantum field theory, geometric representation theory, and $C $-algebras.