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- Maximal_torus abstract "In the mathematical theory of compact Lie groups a special role is played by torus subgroups, in particular by the maximal torus subgroups.A torus in a compact Lie group G is a compact, connected, abelian Lie subgroup of G (and therefore isomorphic to the standard torus Tn). A maximal torus is one which is maximal among such subgroups. That is, T is a maximal torus if for any other torus T′ containing T we have T = T′. Every torus is contained in a maximal torus simply by dimensional considerations. A noncompact Lie group need not have any nontrivial tori (e.g. Rn).The dimension of a maximal torus in G is called the rank of G. The rank is well-defined since all maximal tori turn out to be conjugate. For semisimple groups the rank is equal to the number of nodes in the associated Dynkin diagram.".
- Maximal_torus wikiPageID "360136".
- Maximal_torus wikiPageLength "5843".
- Maximal_torus wikiPageOutDegree "42".
- Maximal_torus wikiPageRevisionID "544861986".
- Maximal_torus wikiPageWikiLink Abelian_group.
- Maximal_torus wikiPageWikiLink Automorphism.
- Maximal_torus wikiPageWikiLink Bruhat_decomposition.
- Maximal_torus wikiPageWikiLink Cartan_subalgebra.
- Maximal_torus wikiPageWikiLink Category:Lie_groups.
- Maximal_torus wikiPageWikiLink Category:Representation_theory_of_Lie_groups.
- Maximal_torus wikiPageWikiLink Centralizer.
- Maximal_torus wikiPageWikiLink Centralizer_and_normalizer.
- Maximal_torus wikiPageWikiLink Closed_set.
- Maximal_torus wikiPageWikiLink Compact_Lie_group.
- Maximal_torus wikiPageWikiLink Compact_group.
- Maximal_torus wikiPageWikiLink Compact_space.
- Maximal_torus wikiPageWikiLink Component_group.
- Maximal_torus wikiPageWikiLink Conjugacy_class.
- Maximal_torus wikiPageWikiLink Conjugate_(group_theory).
- Maximal_torus wikiPageWikiLink Connected_space.
- Maximal_torus wikiPageWikiLink Diagonal_matrices.
- Maximal_torus wikiPageWikiLink Diagonal_matrix.
- Maximal_torus wikiPageWikiLink Dimension.
- Maximal_torus wikiPageWikiLink Dimension_(mathematics_and_physics).
- Maximal_torus wikiPageWikiLink Dynkin_diagram.
- Maximal_torus wikiPageWikiLink Group_action.
- Maximal_torus wikiPageWikiLink Identity_component.
- Maximal_torus wikiPageWikiLink Lie_algebra.
- Maximal_torus wikiPageWikiLink Lie_group.
- Maximal_torus wikiPageWikiLink Lie_subgroup.
- Maximal_torus wikiPageWikiLink Mathematics.
- Maximal_torus wikiPageWikiLink Normalizer.
- Maximal_torus wikiPageWikiLink Orbit_(group_theory).
- Maximal_torus wikiPageWikiLink Orbit_space.
- Maximal_torus wikiPageWikiLink Orthogonal_group.
- Maximal_torus wikiPageWikiLink Outer_automorphism.
- Maximal_torus wikiPageWikiLink Outer_automorphism_group.
- Maximal_torus wikiPageWikiLink Representation_theory.
- Maximal_torus wikiPageWikiLink Rotation.
- Maximal_torus wikiPageWikiLink Rotation_group_SO(3).
- Maximal_torus wikiPageWikiLink Semisimple_Lie_algebra.
- Maximal_torus wikiPageWikiLink Semisimple_Lie_group.
- Maximal_torus wikiPageWikiLink Special_orthogonal_group.
- Maximal_torus wikiPageWikiLink Special_unitary_group.
- Maximal_torus wikiPageWikiLink Symplectic_group.
- Maximal_torus wikiPageWikiLink Toral_Lie_algebra.
- Maximal_torus wikiPageWikiLink Torus.
- Maximal_torus wikiPageWikiLink Unitary_group.
- Maximal_torus wikiPageWikiLink Well-defined.
- Maximal_torus wikiPageWikiLink Weyl_character_formula.
- Maximal_torus wikiPageWikiLink Weyl_denominator_formula.
- Maximal_torus wikiPageWikiLink Weyl_group.
- Maximal_torus wikiPageWikiLinkText "Maximal Torus".
- Maximal_torus wikiPageWikiLinkText "Maximal torus".
- Maximal_torus wikiPageWikiLinkText "maximal tori in Lie groups".
- Maximal_torus wikiPageWikiLinkText "maximal torus".
- Maximal_torus wikiPageWikiLinkText "torus".
- Maximal_torus hasPhotoCollection Maximal_torus.
- Maximal_torus wikiPageUsesTemplate Template:Citation.
- Maximal_torus subject Category:Lie_groups.
- Maximal_torus subject Category:Representation_theory_of_Lie_groups.
- Maximal_torus hypernym Compact.
- Maximal_torus type Weapon.
- Maximal_torus comment "In the mathematical theory of compact Lie groups a special role is played by torus subgroups, in particular by the maximal torus subgroups.A torus in a compact Lie group G is a compact, connected, abelian Lie subgroup of G (and therefore isomorphic to the standard torus Tn). A maximal torus is one which is maximal among such subgroups. That is, T is a maximal torus if for any other torus T′ containing T we have T = T′.".
- Maximal_torus label "Maximal torus".
- Maximal_torus sameAs Tore_maximal.
- Maximal_torus sameAs 極大トーラス.
- Maximal_torus sameAs m.01_bn6.
- Maximal_torus sameAs Максимальный_тор.
- Maximal_torus sameAs Q1000120.
- Maximal_torus sameAs Q1000120.
- Maximal_torus sameAs 極大環面.
- Maximal_torus wasDerivedFrom Maximal_torus?oldid=544861986.
- Maximal_torus isPrimaryTopicOf Maximal_torus.