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- Quantum_group abstract "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 Drinfeld 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.In Drinfeld's approach, quantum groups arise as Hopf algebras depending on an auxiliary parameter q or h, which become universal enveloping algebras of a certain Lie algebra, frequently semisimple or affine, when q = 1 or h = 0. Closely related are certain dual objects, also Hopf algebras and also called quantum groups, deforming the algebra of functions on the corresponding semisimple algebraic group or a compact Lie group.Just as groups often appear as symmetries, quantum groups act on many other mathematical objects and it has become fashionable to introduce the adjective quantum in such cases; for example there are quantum planes and quantum Grassmannians.".
- Quantum_group wikiPageExternalLink 0105002v1.
- Quantum_group wikiPageExternalLink books?id=HKPjCUiOUQ0C&printsec=frontcover.
- Quantum_group wikiPageExternalLink what-is.pdf.
- Quantum_group wikiPageID "340678".
- Quantum_group wikiPageRevisionID "605700297".
- Quantum_group hasPhotoCollection Quantum_group.
- Quantum_group subject Category:Mathematical_quantization.
- Quantum_group subject Category:Quantum_groups.
- Quantum_group type Abstraction100002137.
- Quantum_group type Group100031264.
- Quantum_group type QuantumGroups.
- Quantum_group comment "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.".
- Quantum_group label "Groupe quantique".
- Quantum_group label "Gruppo quantico".
- Quantum_group label "Kwantumgroep".
- Quantum_group label "Quantengruppe".
- Quantum_group label "Quantum group".
- Quantum_group label "Квантовая группа".
- Quantum_group label "量子群".
- Quantum_group sameAs Quantengruppe.
- Quantum_group sameAs Groupe_quantique.
- Quantum_group sameAs Gruppo_quantico.
- Quantum_group sameAs 양자군.
- Quantum_group sameAs Kwantumgroep.
- Quantum_group sameAs m.01y0_5.
- Quantum_group sameAs Q2122223.
- Quantum_group sameAs Q2122223.
- Quantum_group sameAs Quantum_group.
- Quantum_group wasDerivedFrom Quantum_group?oldid=605700297.
- Quantum_group isPrimaryTopicOf Quantum_group.