Книга: Quantum Group: Mathematics, Theoretical Physics, Ring Theory, Hopf Algebra, Integrable System, Lie Group, Algebraic Group, Compact Group, Universal Enveloping Algebra

High Quality Content by WIKIPEDIA articles! In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebra with additional structure. In general, a quantum group is some kind of Hopf algebra. There is no single, all-encompassing definition, but instead a family of broadly similar objects. The term 'quantum group' often denotes a kind of noncommutative algebra with additional structure that first appeared in the theory of quantum integrable systems, and which was then formalized by Vladimir Drinfel'd and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a 'bicrossproduct' class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo.