Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Lie_algebra_extension> ?p ?o }
- Lie_algebra_extension abstract "In the theory of Lie groups, Lie algebras and their representation theory, a Lie algebra extension e is an enlargement of a given Lie algebra g by another Lie algebra h. Extensions arise in several ways. There is the trivial extension obtained by taking a direct sum of two Lie algebras. Other types are the split extension and the central extension. Extensions may arise naturally, for instance, when forming a Lie algebra from projective group representations. Such a Lie algebra will contain central charges.Starting with a polynomial loop algebra over finite-dimensional simple Lie algebra and performing two extensions, a central extension and an extension by a derivation, one obtains a Lie algebra which is isomorphic with an untwisted affine Kac–Moody algebra. Using the centrally extended loop algebra algebra one may construct a current algebra in two spacetime dimensions. The Virasoro algebra is the universal central extension of the Witt algebra.Central extensions are needed in physics, because the symmetry group of a quantized system usually is a central extension of the classical symmetry group, and in the same way the corresponding symmetry Lie algebra of the quantum system is, in general, a central extension of the classical symmetry algebra. Kac–Moody algebras have been conjectured to be a symmetry groups of a unified superstring theory. The centrally extended Lie algebras play a dominant role in quantum field theory, particularly in conformal field theory, string theory and in M-theory.A large portion towards the end is devoted to background material for applications of Lie algebra extensions, both in mathematics and in physics, in areas where they are actually useful. A parenthetical link, (background material), is provided where it might be beneficial.".
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- Lie_algebra_extension wikiPageWikiLink Adjoint_representation.
- Lie_algebra_extension wikiPageWikiLink Adjoint_representation_of_a_Lie_algebra.
- Lie_algebra_extension wikiPageWikiLink Alternatization.
- Lie_algebra_extension wikiPageWikiLink Automorphism.
- Lie_algebra_extension wikiPageWikiLink Baker–Campbell–Hausdorff_formula.
- Lie_algebra_extension wikiPageWikiLink Basis_(linear_algebra).
- Lie_algebra_extension wikiPageWikiLink Bilinear_map.
- Lie_algebra_extension wikiPageWikiLink Birkhäuser.
- Lie_algebra_extension wikiPageWikiLink Cambridge_University_Press.
- Lie_algebra_extension wikiPageWikiLink Cartans_criterion.
- Lie_algebra_extension wikiPageWikiLink Category:Conformal_field_theory.
- Lie_algebra_extension wikiPageWikiLink Category:Lie_algebras.
- Lie_algebra_extension wikiPageWikiLink Category:Lie_groups.
- Lie_algebra_extension wikiPageWikiLink Category:Mathematical_physics.
- Lie_algebra_extension wikiPageWikiLink Category:Quantum_field_theory.
- Lie_algebra_extension wikiPageWikiLink Category:String_theory.
- Lie_algebra_extension wikiPageWikiLink Center_(algebra).
- Lie_algebra_extension wikiPageWikiLink Center_(group_theory).
- Lie_algebra_extension wikiPageWikiLink Central_charge.
- Lie_algebra_extension wikiPageWikiLink Classical_field_theory.
- Lie_algebra_extension wikiPageWikiLink Classical_group.
- Lie_algebra_extension wikiPageWikiLink Conformal_field_theory.
- Lie_algebra_extension wikiPageWikiLink Conserved_current.
- Lie_algebra_extension wikiPageWikiLink Continuous_symmetry.
- Lie_algebra_extension wikiPageWikiLink Covering_group.
- Lie_algebra_extension wikiPageWikiLink Creation_and_annihilation_operators.
- Lie_algebra_extension wikiPageWikiLink Current_algebra.
- Lie_algebra_extension wikiPageWikiLink Einstein_notation.
- Lie_algebra_extension wikiPageWikiLink Elsevier.
- Lie_algebra_extension wikiPageWikiLink Epimorphism.
- Lie_algebra_extension wikiPageWikiLink Equivalence_relation.
- Lie_algebra_extension wikiPageWikiLink Ernst_Witt.
- Lie_algebra_extension wikiPageWikiLink Exact_sequence.
- Lie_algebra_extension wikiPageWikiLink Exponential_map_(Lie_theory).
- Lie_algebra_extension wikiPageWikiLink Fiber_(mathematics).
- Lie_algebra_extension wikiPageWikiLink Field_(mathematics).
- Lie_algebra_extension wikiPageWikiLink File:Lie_algebra_extension_figure_1.svg.
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- Lie_algebra_extension wikiPageWikiLink Galilean_transformation.
- Lie_algebra_extension wikiPageWikiLink Gauge_theory.
- Lie_algebra_extension wikiPageWikiLink Group_action.
- Lie_algebra_extension wikiPageWikiLink Group_cohomology.
- Lie_algebra_extension wikiPageWikiLink Group_contraction.
- Lie_algebra_extension wikiPageWikiLink Group_extension.
- Lie_algebra_extension wikiPageWikiLink Hamiltonian_(quantum_mechanics).
- Lie_algebra_extension wikiPageWikiLink Heisenberg_group.
- Lie_algebra_extension wikiPageWikiLink Heisenberg_picture.
- Lie_algebra_extension wikiPageWikiLink Ideal_(ring_theory).
- Lie_algebra_extension wikiPageWikiLink Integration_by_parts.
- Lie_algebra_extension wikiPageWikiLink JSTOR.
- Lie_algebra_extension wikiPageWikiLink Kac–Moody_algebra.
- Lie_algebra_extension wikiPageWikiLink Lagrangian_(field_theory).
- Lie_algebra_extension wikiPageWikiLink Lagrangian_mechanics.
- Lie_algebra_extension wikiPageWikiLink Laurent_polynomial.
- Lie_algebra_extension wikiPageWikiLink Lie_algebra.
- Lie_algebra_extension wikiPageWikiLink Lie_algebra_cohomology.
- Lie_algebra_extension wikiPageWikiLink Lie_algebra_representation.
- Lie_algebra_extension wikiPageWikiLink Lie_group.
- Lie_algebra_extension wikiPageWikiLink Lie_group–Lie_algebra_correspondence.
- Lie_algebra_extension wikiPageWikiLink Lies_third_theorem.
- Lie_algebra_extension wikiPageWikiLink Light-cone_coordinates.
- Lie_algebra_extension wikiPageWikiLink Light_cone_gauge.
- Lie_algebra_extension wikiPageWikiLink Loop_algebra.
- Lie_algebra_extension wikiPageWikiLink Loop_group.
- Lie_algebra_extension wikiPageWikiLink Lorentz_group.
- Lie_algebra_extension wikiPageWikiLink M-theory.
- Lie_algebra_extension wikiPageWikiLink Manifold.
- Lie_algebra_extension wikiPageWikiLink Miguel_Ángel_Virasoro_(physicist).
- Lie_algebra_extension wikiPageWikiLink Monomorphism.
- Lie_algebra_extension wikiPageWikiLink Nambu–Goto_action.
- Lie_algebra_extension wikiPageWikiLink Neumann_boundary_condition.
- Lie_algebra_extension wikiPageWikiLink Noethers_theorem.
- Lie_algebra_extension wikiPageWikiLink Normal_order.
- Lie_algebra_extension wikiPageWikiLink Null_vector.
- Lie_algebra_extension wikiPageWikiLink Orthogonal_group.
- Lie_algebra_extension wikiPageWikiLink Otto_Hölder.
- Lie_algebra_extension wikiPageWikiLink Otto_Schreier.
- Lie_algebra_extension wikiPageWikiLink Planck_constant.
- Lie_algebra_extension wikiPageWikiLink Poincaré_group.
- Lie_algebra_extension wikiPageWikiLink Poisson_summation_formula.
- Lie_algebra_extension wikiPageWikiLink Principal_bundle.
- Lie_algebra_extension wikiPageWikiLink Product_rule.
- Lie_algebra_extension wikiPageWikiLink Projective_representation.
- Lie_algebra_extension wikiPageWikiLink Quantization_(physics).
- Lie_algebra_extension wikiPageWikiLink Quantum_field_theory.
- Lie_algebra_extension wikiPageWikiLink Quantum_number.
- Lie_algebra_extension wikiPageWikiLink Recurrence_relation.
- Lie_algebra_extension wikiPageWikiLink Riesz_representation_theorem.
- Lie_algebra_extension wikiPageWikiLink Robert_Moody.
- Lie_algebra_extension wikiPageWikiLink Scalar_field.
- Lie_algebra_extension wikiPageWikiLink Schrödinger_equation.