Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Quantum_group> ?p ?o }
- 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" first appeared in the theory of quantum integrable systems, 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.
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- Quantum_group wikiPageRevisionID "672594502".
- Quantum_group wikiPageWikiLink Adjoint_endomorphism.
- Quantum_group wikiPageWikiLink Adjoint_representation_of_a_Lie_algebra.
- Quantum_group wikiPageWikiLink Affine_Lie_algebra.
- Quantum_group wikiPageWikiLink Affine_quantum_group.
- Quantum_group wikiPageWikiLink Alain_Connes.
- Quantum_group wikiPageWikiLink Algebra_over_a_field.
- Quantum_group wikiPageWikiLink Algebraic_group.
- Quantum_group wikiPageWikiLink Associative_algebra.
- Quantum_group wikiPageWikiLink Bicrossproduct.
- Quantum_group wikiPageWikiLink Born_reciprocity.
- Quantum_group wikiPageWikiLink Braid_group.
- Quantum_group wikiPageWikiLink Braid_theory.
- Quantum_group wikiPageWikiLink Braided_vector_space.
- Quantum_group wikiPageWikiLink C*-algebra.
- Quantum_group wikiPageWikiLink Cambridge_University_Press.
- Quantum_group wikiPageWikiLink Cartan_matrix.
- Quantum_group wikiPageWikiLink Category:Mathematical_quantization.
- Quantum_group wikiPageWikiLink Category:Quantum_groups.
- Quantum_group wikiPageWikiLink Coalgebra.
- Quantum_group wikiPageWikiLink Cocommutative.
- Quantum_group wikiPageWikiLink Commutative.
- Quantum_group wikiPageWikiLink Commutative_property.
- Quantum_group wikiPageWikiLink Compact_Lie_group.
- Quantum_group wikiPageWikiLink Compact_group.
- Quantum_group wikiPageWikiLink Compact_quantum_group.
- Quantum_group wikiPageWikiLink Counit.
- Quantum_group wikiPageWikiLink Crystal_base.
- Quantum_group wikiPageWikiLink Dynkin_diagram.
- Quantum_group wikiPageWikiLink Euclidean_group.
- Quantum_group wikiPageWikiLink Factorial.
- Quantum_group wikiPageWikiLink Gelfand_representation.
- Quantum_group wikiPageWikiLink Group_algebra.
- Quantum_group wikiPageWikiLink Group_representation.
- Quantum_group wikiPageWikiLink Heisenberg_algebra.
- Quantum_group wikiPageWikiLink Heisenberg_group.
- Quantum_group wikiPageWikiLink Highest_weight_representation.
- Quantum_group wikiPageWikiLink Homeomorphism.
- Quantum_group wikiPageWikiLink Hopf_algebra.
- Quantum_group wikiPageWikiLink Hopf_algebras.
- Quantum_group wikiPageWikiLink Integrable_system.
- Quantum_group wikiPageWikiLink Inverse_element.
- Quantum_group wikiPageWikiLink Invertible.
- Quantum_group wikiPageWikiLink Jean-Pierre_Serre.
- Quantum_group wikiPageWikiLink Kac–Moody_algebra.
- Quantum_group wikiPageWikiLink Knot_(mathematics).
- Quantum_group wikiPageWikiLink Kronecker_delta.
- Quantum_group wikiPageWikiLink Lie_algebra.
- Quantum_group wikiPageWikiLink Lie_algebras.
- Quantum_group wikiPageWikiLink Lie_bialgebra.
- Quantum_group wikiPageWikiLink Lie_group.
- Quantum_group wikiPageWikiLink Lie_groups.
- Quantum_group wikiPageWikiLink Link_(knot_theory).
- Quantum_group wikiPageWikiLink Ludvig_Faddeev.
- Quantum_group wikiPageWikiLink Ludwig_Faddeev.
- Quantum_group wikiPageWikiLink Masaki_Kashiwara.
- Quantum_group wikiPageWikiLink Mathematics.
- Quantum_group wikiPageWikiLink Michio_Jimbo.
- Quantum_group wikiPageWikiLink Module_(mathematics).
- Quantum_group wikiPageWikiLink Nichols_algebra.
- Quantum_group wikiPageWikiLink Nicolai_Reshetikhin.
- Quantum_group wikiPageWikiLink Noncommutative_algebra.
- Quantum_group wikiPageWikiLink Noncommutative_geometry.
- Quantum_group wikiPageWikiLink Noncommutative_ring.
- Quantum_group wikiPageWikiLink Notices_of_the_American_Mathematical_Society.
- Quantum_group wikiPageWikiLink PDF.
- Quantum_group wikiPageWikiLink Poincaré–Birkhoff–Witt_theorem.
- Quantum_group wikiPageWikiLink Poisson–Lie_group.
- Quantum_group wikiPageWikiLink Polynomial.
- Quantum_group wikiPageWikiLink Portable_Document_Format.
- Quantum_group wikiPageWikiLink Q-Pochhammer_symbol.
- Quantum_group wikiPageWikiLink Q-analog.
- Quantum_group wikiPageWikiLink Q-factorial.
- Quantum_group wikiPageWikiLink Q-number.
- Quantum_group wikiPageWikiLink Quantum_Grassmannian.
- Quantum_group wikiPageWikiLink Quantum_affine_algebra.
- Quantum_group wikiPageWikiLink Quantum_affine_algebras.
- Quantum_group wikiPageWikiLink Quantum_gravity.
- Quantum_group wikiPageWikiLink Quantum_inverse_scattering_method.
- Quantum_group wikiPageWikiLink Quantum_number.
- Quantum_group wikiPageWikiLink Quantum_plane.
- Quantum_group wikiPageWikiLink Quasitriangular_Hopf_algebra.
- Quantum_group wikiPageWikiLink Rational_function.
- Quantum_group wikiPageWikiLink Root_lattice.
- Quantum_group wikiPageWikiLink Root_system.
- Quantum_group wikiPageWikiLink S.L._Woronowicz.
- Quantum_group wikiPageWikiLink S._L._Woronowicz.
- Quantum_group wikiPageWikiLink Semisimple_Lie_algebra.
- Quantum_group wikiPageWikiLink Shahn_Majid.
- Quantum_group wikiPageWikiLink Simple_root_(polynomial).
- Quantum_group wikiPageWikiLink Springer-Verlag.
- Quantum_group wikiPageWikiLink Springer_Science+Business_Media.
- Quantum_group wikiPageWikiLink Tensor_product.