Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Hermitian_symmetric_space> ?p ?o }
- Hermitian_symmetric_space abstract "In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has as an inversion symmetry preserving the Hermitian structure. First studied by Élie Cartan, they form a natural generalization of the notion of Riemannian symmetric space from real manifolds to complex manifolds.Every Hermitian symmetric space is a homogeneous space for its isometry group and has a unique decomposition as a product of irreducible spaces and a Euclidean space. The irreducible spaces arise in pairs as a non-compact space that, as Borel showed, can be embedded as an open subspace of its compact dual space. Harish Chandra showed that each non-compact space can be realized as a bounded symmetric domain in a complex vector space. The simplest case involves the groups SU(2), SU(1,1) and their common complexification SL(2,C). In this case the non-compact space is the unit disk, a homogeneous space for SU(1,1). It is a bounded domain in the complex plane C. The one-point compactification of C, the Riemann sphere, is the dual space, a homogeneous space for SU(2) and SL(2,C).Irreducible compact Hermitian symmetric spaces are exactly the homogeneous spaces of simple compact Lie groups by maximal closed connected subgroups which contain a maximal torus and have center isomorphic to T. There is a complete classification of irreducible spaces, with four classical series, studied by Cartan, and two exceptional cases; the classification can be deduced fromBorel–de Siebenthal theory, which classifies closed connected subgroups containing a maximal torus. Hermitian symmetric spaces appear in the theory of Jordan triple systems, several complex variables, complex geometry, automorphic forms and group representations, in particular permitting the construction of the holomorphic discrete series representations of semisimple Lie groups.".
- Hermitian_symmetric_space wikiPageExternalLink lecturenotesinma19691rice.
- Hermitian_symmetric_space wikiPageExternalLink irvine.pdf.
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- Hermitian_symmetric_space wikiPageWikiLink Adjoint_representation.
- Hermitian_symmetric_space wikiPageWikiLink Algebraic_group.
- Hermitian_symmetric_space wikiPageWikiLink Algebraic_groups.
- Hermitian_symmetric_space wikiPageWikiLink Almost_complex_manifold.
- Hermitian_symmetric_space wikiPageWikiLink Almost_complex_structure.
- Hermitian_symmetric_space wikiPageWikiLink Armand_Borel.
- Hermitian_symmetric_space wikiPageWikiLink Automorphic_form.
- Hermitian_symmetric_space wikiPageWikiLink Baily–Borel_compactification.
- Hermitian_symmetric_space wikiPageWikiLink Bergman_kernel.
- Hermitian_symmetric_space wikiPageWikiLink Bergman_metric.
- Hermitian_symmetric_space wikiPageWikiLink Biholomorphism.
- Hermitian_symmetric_space wikiPageWikiLink Borel-de_Siebenthal_theory.
- Hermitian_symmetric_space wikiPageWikiLink Borel_subgroup.
- Hermitian_symmetric_space wikiPageWikiLink Borel–de_Siebenthal_theory.
- Hermitian_symmetric_space wikiPageWikiLink Bounded_symmetric_domain.
- Hermitian_symmetric_space wikiPageWikiLink Carl_Ludwig_Siegel.
- Hermitian_symmetric_space wikiPageWikiLink Category:Complex_manifolds.
- Hermitian_symmetric_space wikiPageWikiLink Category:Differential_geometry.
- Hermitian_symmetric_space wikiPageWikiLink Category:Homogeneous_spaces.
- Hermitian_symmetric_space wikiPageWikiLink Category:Lie_groups.
- Hermitian_symmetric_space wikiPageWikiLink Category:Riemannian_geometry.
- Hermitian_symmetric_space wikiPageWikiLink Cauchy_integral_formula.
- Hermitian_symmetric_space wikiPageWikiLink Cauchys_integral_formula.
- Hermitian_symmetric_space wikiPageWikiLink Cayley_algebra.
- Hermitian_symmetric_space wikiPageWikiLink Cayley_plane.
- Hermitian_symmetric_space wikiPageWikiLink Cayley_projective_plane.
- Hermitian_symmetric_space wikiPageWikiLink Cayley_transform.
- Hermitian_symmetric_space wikiPageWikiLink Compact_space.
- Hermitian_symmetric_space wikiPageWikiLink Complete_metric_space.
- Hermitian_symmetric_space wikiPageWikiLink Complex_geometry.
- Hermitian_symmetric_space wikiPageWikiLink Complex_manifold.
- Hermitian_symmetric_space wikiPageWikiLink Complex_projective_space.
- Hermitian_symmetric_space wikiPageWikiLink Complex_vector_space.
- Hermitian_symmetric_space wikiPageWikiLink Complexification_(Lie_group).
- Hermitian_symmetric_space wikiPageWikiLink Composition_algebra.
- Hermitian_symmetric_space wikiPageWikiLink Convex_set.
- Hermitian_symmetric_space wikiPageWikiLink Domain_(mathematics).
- Hermitian_symmetric_space wikiPageWikiLink Domain_of_a_function.
- Hermitian_symmetric_space wikiPageWikiLink Euclidean_Hurwitz_algebra.
- Hermitian_symmetric_space wikiPageWikiLink Euler_characteristic.
- Hermitian_symmetric_space wikiPageWikiLink Euler–Poincaré_characteristic.
- Hermitian_symmetric_space wikiPageWikiLink Freudenthal_magic_square.
- Hermitian_symmetric_space wikiPageWikiLink Fubini–Study_metric.
- Hermitian_symmetric_space wikiPageWikiLink Generalized_flag_manifold.
- Hermitian_symmetric_space wikiPageWikiLink Generalized_flag_variety.
- Hermitian_symmetric_space wikiPageWikiLink Glossary_of_Riemannian_and_metric_geometry.
- Hermitian_symmetric_space wikiPageWikiLink Graded_Lie_algebra.
- Hermitian_symmetric_space wikiPageWikiLink Grassmannian.
- Hermitian_symmetric_space wikiPageWikiLink Group_action.
- Hermitian_symmetric_space wikiPageWikiLink Group_representation.
- Hermitian_symmetric_space wikiPageWikiLink Harish-Chandra.
- Hermitian_symmetric_space wikiPageWikiLink Harish_Chandra.
- Hermitian_symmetric_space wikiPageWikiLink Hermitian_manifold.
- Hermitian_symmetric_space wikiPageWikiLink Hermitian_metric.
- Hermitian_symmetric_space wikiPageWikiLink Hermitian_symmetric_space.
- Hermitian_symmetric_space wikiPageWikiLink Holomorphic_discrete_series_representation.
- Hermitian_symmetric_space wikiPageWikiLink Hurwitzs_theorem_(composition_algebras).
- Hermitian_symmetric_space wikiPageWikiLink Identity_component.
- Hermitian_symmetric_space wikiPageWikiLink Invariant_convex_cone.
- Hermitian_symmetric_space wikiPageWikiLink Jordan_frame_(Jordan_algebra).
- Hermitian_symmetric_space wikiPageWikiLink Jordan_pair.
- Hermitian_symmetric_space wikiPageWikiLink Jordan_triple_system.
- Hermitian_symmetric_space wikiPageWikiLink Killing_form.
- Hermitian_symmetric_space wikiPageWikiLink Kähler_manifold.
- Hermitian_symmetric_space wikiPageWikiLink Levi_decomposition.
- Hermitian_symmetric_space wikiPageWikiLink Levi_factor.
- Hermitian_symmetric_space wikiPageWikiLink Lexicographic_order.
- Hermitian_symmetric_space wikiPageWikiLink Lexicographical_order.
- Hermitian_symmetric_space wikiPageWikiLink Lie_algebra.
- Hermitian_symmetric_space wikiPageWikiLink Lie_group.
- Hermitian_symmetric_space wikiPageWikiLink Manifold.
- Hermitian_symmetric_space wikiPageWikiLink Mathematics.
- Hermitian_symmetric_space wikiPageWikiLink Mutation_(Jordan_algebra).
- Hermitian_symmetric_space wikiPageWikiLink Möbius_transformation.
- Hermitian_symmetric_space wikiPageWikiLink Nilradical_of_a_Lie_algebra.
- Hermitian_symmetric_space wikiPageWikiLink Octonion_algebra.
- Hermitian_symmetric_space wikiPageWikiLink Operator_norm.
- Hermitian_symmetric_space wikiPageWikiLink Orthogonal_symmetric_Lie_algebra.
- Hermitian_symmetric_space wikiPageWikiLink Parabolic_subgroup.
- Hermitian_symmetric_space wikiPageWikiLink Polar_decomposition.
- Hermitian_symmetric_space wikiPageWikiLink Projective_variety.
- Hermitian_symmetric_space wikiPageWikiLink Real_manifold.
- Hermitian_symmetric_space wikiPageWikiLink Restricted_root_system.
- Hermitian_symmetric_space wikiPageWikiLink Riemann_sphere.
- Hermitian_symmetric_space wikiPageWikiLink Riemannian_manifold.
- Hermitian_symmetric_space wikiPageWikiLink Riemannian_metric.
- Hermitian_symmetric_space wikiPageWikiLink Riemannian_symmetric_space.
- Hermitian_symmetric_space wikiPageWikiLink Robert_Hermann_(mathematician).
- Hermitian_symmetric_space wikiPageWikiLink Rosenfeld_projective_plane.
- Hermitian_symmetric_space wikiPageWikiLink Semisimple_Lie_algebra.
- Hermitian_symmetric_space wikiPageWikiLink Semisimple_Lie_group.
- Hermitian_symmetric_space wikiPageWikiLink Several_complex_variables.