Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Lie_theory> ?p ?o }
- Lie_theory abstract "In mathematics, the investigator Sophus Lie (/ˈliː/ LEE) initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory. For instance, the latter subject is Lie sphere geometry. This article addresses his approach to transformation groups, which is one of the areas of mathematics, and was worked out by Wilhelm Killing and Élie Cartan. The foundation of Lie theory is the exponential map relating Lie algebras to Lie groups which is called the Lie group–Lie algebra correspondence. The subject is part of differential geometry since Lie groups are differentiable manifolds. Lie groups evolve out of the identity (1) and the tangent vectors to one-parameter subgroups generate the Lie algebra. The structure of a Lie group is implicit in its algebra, and the structure of the Lie algebra is expressed by root systems and root data.Lie theory has been particularly useful in mathematical physics since it describes important physical groups such as the Galilean group, the Lorentz group and the Poincaré group.".
- Lie_theory wikiPageExternalLink S0002-9904-1959-10358-X.
- Lie_theory wikiPageExternalLink jltcover.htm.
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- Lie_theory wikiPageWikiLink 2_×_2_real_matrices.
- Lie_theory wikiPageWikiLink 3-sphere.
- Lie_theory wikiPageWikiLink Academic_Press.
- Lie_theory wikiPageWikiLink Algebraic_equation.
- Lie_theory wikiPageWikiLink American_Mathematical_Society.
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- Lie_theory wikiPageWikiLink Areas_of_mathematics.
- Lie_theory wikiPageWikiLink Building_(mathematics).
- Lie_theory wikiPageWikiLink Bulletin_of_the_American_Mathematical_Society.
- Lie_theory wikiPageWikiLink Cambridge_University_Press.
- Lie_theory wikiPageWikiLink Category:Differential_equations.
- Lie_theory wikiPageWikiLink Category:History_of_mathematics.
- Lie_theory wikiPageWikiLink Category:Lie_groups.
- Lie_theory wikiPageWikiLink Classical_group.
- Lie_theory wikiPageWikiLink Commutator.
- Lie_theory wikiPageWikiLink Compact_space.
- Lie_theory wikiPageWikiLink Complex_plane.
- Lie_theory wikiPageWikiLink Contact_(mathematics).
- Lie_theory wikiPageWikiLink Coxeter_group.
- Lie_theory wikiPageWikiLink Cross_product.
- Lie_theory wikiPageWikiLink David_Hilbert.
- Lie_theory wikiPageWikiLink Differentiable_manifold.
- Lie_theory wikiPageWikiLink Differential_equation.
- Lie_theory wikiPageWikiLink Differential_form.
- Lie_theory wikiPageWikiLink Differential_geometry.
- Lie_theory wikiPageWikiLink Discrete_group.
- Lie_theory wikiPageWikiLink Dover_Publications.
- Lie_theory wikiPageWikiLink Dual_number.
- Lie_theory wikiPageWikiLink Eulers_formula.
- Lie_theory wikiPageWikiLink Exponential_map_(Lie_theory).
- Lie_theory wikiPageWikiLink Felix_Klein.
- Lie_theory wikiPageWikiLink Friedrich_Engel_(mathematician).
- Lie_theory wikiPageWikiLink Galilean_transformation.
- Lie_theory wikiPageWikiLink Galois_theory.
- Lie_theory wikiPageWikiLink Georg_Scheffers.
- Lie_theory wikiPageWikiLink Group_action.
- Lie_theory wikiPageWikiLink Group_of_Lie_type.
- Lie_theory wikiPageWikiLink Heisenberg_group.
- Lie_theory wikiPageWikiLink Henri_Poincaré.
- Lie_theory wikiPageWikiLink Hermann_Weyl.
- Lie_theory wikiPageWikiLink Hilberts_fifth_problem.
- Lie_theory wikiPageWikiLink Hyperbolic_angle.
- Lie_theory wikiPageWikiLink International_Congress_of_Mathematicians.
- Lie_theory wikiPageWikiLink Julian_Coolidge.
- Lie_theory wikiPageWikiLink Lie_algebra.
- Lie_theory wikiPageWikiLink Lie_group.
- Lie_theory wikiPageWikiLink Lie_group–Lie_algebra_correspondence.
- Lie_theory wikiPageWikiLink Lie_sphere_geometry.
- Lie_theory wikiPageWikiLink Linear_algebraic_group.
- Lie_theory wikiPageWikiLink List_of_Lie_groups_topics.
- Lie_theory wikiPageWikiLink Lorentz_group.
- Lie_theory wikiPageWikiLink Mathematical_physics.
- Lie_theory wikiPageWikiLink Mathematics.
- Lie_theory wikiPageWikiLink Modular_form.
- Lie_theory wikiPageWikiLink Moving_frame.
- Lie_theory wikiPageWikiLink One-parameter_group.
- Lie_theory wikiPageWikiLink Ordinary_differential_equation.
- Lie_theory wikiPageWikiLink Oxford_University_Press.
- Lie_theory wikiPageWikiLink Paul_Cohn.
- Lie_theory wikiPageWikiLink Poincaré_group.
- Lie_theory wikiPageWikiLink Polar_decomposition.
- Lie_theory wikiPageWikiLink Quaternion.
- Lie_theory wikiPageWikiLink Root_datum.
- Lie_theory wikiPageWikiLink Root_system.
- Lie_theory wikiPageWikiLink Semisimple_Lie_algebra.
- Lie_theory wikiPageWikiLink Slope.
- Lie_theory wikiPageWikiLink Sophus_Lie.
- Lie_theory wikiPageWikiLink Sphere.
- Lie_theory wikiPageWikiLink Split-complex_number.
- Lie_theory wikiPageWikiLink Symmetry.
- Lie_theory wikiPageWikiLink Tangent_vector.
- Lie_theory wikiPageWikiLink The_Mathematical_Intelligencer.
- Lie_theory wikiPageWikiLink Unit_hyperbola.
- Lie_theory wikiPageWikiLink Vector_calculus.
- Lie_theory wikiPageWikiLink Versor.
- Lie_theory wikiPageWikiLink Weyl_group.
- Lie_theory wikiPageWikiLink Wilhelm_Killing.
- Lie_theory wikiPageWikiLink Élie_Cartan.
- Lie_theory wikiPageWikiLinkText "Lie Theory".
- Lie_theory wikiPageWikiLinkText "Lie theory".
- Lie_theory wikiPageWikiLinkText "Lie-theoretic method".
- Lie_theory wikiPageUsesTemplate Template:Areas_of_mathematics.
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- Lie_theory wikiPageUsesTemplate Template:Cite_journal.
- Lie_theory wikiPageUsesTemplate Template:IPAc-en.
- Lie_theory wikiPageUsesTemplate Template:Reflist.
- Lie_theory wikiPageUsesTemplate Template:Respell.
- Lie_theory subject Category:Differential_equations.
- Lie_theory subject Category:History_of_mathematics.
- Lie_theory subject Category:Lie_groups.
- Lie_theory type Redirect.
- Lie_theory comment "In mathematics, the investigator Sophus Lie (/ˈliː/ LEE) initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory. For instance, the latter subject is Lie sphere geometry. This article addresses his approach to transformation groups, which is one of the areas of mathematics, and was worked out by Wilhelm Killing and Élie Cartan.".
- Lie_theory label "Lie theory".