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- Compact_Lie_algebra abstract "In the mathematical field of Lie theory, there are two definitions of a compact Lie algebra. Extrinsically and topologically, a compact Lie algebra is the Lie algebra of a compact Lie group; this definition includes tori. Intrinsically and algebraically, a compact Lie algebra is a real Lie algebra whose Killing form is negative definite; this definition is more restrictive and excludes tori, though allowing negative semidefinite includes tori and agrees with the previous definition. A compact Lie algebra can be seen as the smallest real form of a corresponding complex Lie algebra, namely the complexification.".
- Compact_Lie_algebra wikiPageExternalLink l058610.htm.
- Compact_Lie_algebra wikiPageID "25262324".
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- Compact_Lie_algebra wikiPageOutDegree "35".
- Compact_Lie_algebra wikiPageRevisionID "582094399".
- Compact_Lie_algebra wikiPageWikiLink Ados_theorem.
- Compact_Lie_algebra wikiPageWikiLink Category:Properties_of_Lie_algebras.
- Compact_Lie_algebra wikiPageWikiLink Compact_Lie_group.
- Compact_Lie_algebra wikiPageWikiLink Compact_group.
- Compact_Lie_algebra wikiPageWikiLink Compact_real_form.
- Compact_Lie_algebra wikiPageWikiLink Compact_symplectic_group.
- Compact_Lie_algebra wikiPageWikiLink Definite_quadratic_form.
- Compact_Lie_algebra wikiPageWikiLink Dynkin_diagram.
- Compact_Lie_algebra wikiPageWikiLink Exceptional_isomorphism.
- Compact_Lie_algebra wikiPageWikiLink Inner_product.
- Compact_Lie_algebra wikiPageWikiLink Inner_product_space.
- Compact_Lie_algebra wikiPageWikiLink Killing_form.
- Compact_Lie_algebra wikiPageWikiLink Lie_algebra.
- Compact_Lie_algebra wikiPageWikiLink Lie_theory.
- Compact_Lie_algebra wikiPageWikiLink Mathematical.
- Compact_Lie_algebra wikiPageWikiLink Mathematics.
- Compact_Lie_algebra wikiPageWikiLink Negative_definite.
- Compact_Lie_algebra wikiPageWikiLink Negative_semidefinite.
- Compact_Lie_algebra wikiPageWikiLink Orthogonal_group.
- Compact_Lie_algebra wikiPageWikiLink Orthogonal_transformation.
- Compact_Lie_algebra wikiPageWikiLink Projective_orthogonal_group.
- Compact_Lie_algebra wikiPageWikiLink Projective_special_orthogonal_group.
- Compact_Lie_algebra wikiPageWikiLink Projective_special_unitary_group.
- Compact_Lie_algebra wikiPageWikiLink Projective_unitary_group.
- Compact_Lie_algebra wikiPageWikiLink Real_form.
- Compact_Lie_algebra wikiPageWikiLink Real_form_(Lie_theory).
- Compact_Lie_algebra wikiPageWikiLink Reductive_Lie_algebra.
- Compact_Lie_algebra wikiPageWikiLink Satake_diagram.
- Compact_Lie_algebra wikiPageWikiLink Semisimple_Lie_algebra.
- Compact_Lie_algebra wikiPageWikiLink Skew-symmetric_matrices.
- Compact_Lie_algebra wikiPageWikiLink Skew-symmetric_matrix.
- Compact_Lie_algebra wikiPageWikiLink Special_orthogonal_group.
- Compact_Lie_algebra wikiPageWikiLink Special_unitary_group.
- Compact_Lie_algebra wikiPageWikiLink Split_Lie_algebra.
- Compact_Lie_algebra wikiPageWikiLink Symplectic_group.
- Compact_Lie_algebra wikiPageWikiLink Unit_quaternion.
- Compact_Lie_algebra wikiPageWikiLink Versor.
- Compact_Lie_algebra wikiPageWikiLink Vladimir_L._Popov.
- Compact_Lie_algebra wikiPageWikiLink Vladimir_Leonidovich_Popov.
- Compact_Lie_algebra wikiPageWikiLink File:Dynkin_Diagram_Isomorphisms.svg.
- Compact_Lie_algebra wikiPageWikiLinkText "Compact Lie algebra".
- Compact_Lie_algebra wikiPageWikiLinkText "compact Lie algebra".
- Compact_Lie_algebra wikiPageWikiLinkText "compact subalgebra".
- Compact_Lie_algebra wikiPageWikiLinkText "compact".
- Compact_Lie_algebra hasPhotoCollection Compact_Lie_algebra.
- Compact_Lie_algebra wikiPageUsesTemplate Template:Citation.
- Compact_Lie_algebra wikiPageUsesTemplate Template:Lie_groups.
- Compact_Lie_algebra wikiPageUsesTemplate Template:Refbegin.
- Compact_Lie_algebra wikiPageUsesTemplate Template:Refend.
- Compact_Lie_algebra wikiPageUsesTemplate Template:Reflist.
- Compact_Lie_algebra subject Category:Properties_of_Lie_algebras.
- Compact_Lie_algebra hypernym Definitions.
- Compact_Lie_algebra type Book.
- Compact_Lie_algebra type Algebra.
- Compact_Lie_algebra type Property.
- Compact_Lie_algebra comment "In the mathematical field of Lie theory, there are two definitions of a compact Lie algebra. Extrinsically and topologically, a compact Lie algebra is the Lie algebra of a compact Lie group; this definition includes tori. Intrinsically and algebraically, a compact Lie algebra is a real Lie algebra whose Killing form is negative definite; this definition is more restrictive and excludes tori, though allowing negative semidefinite includes tori and agrees with the previous definition.".
- Compact_Lie_algebra label "Compact Lie algebra".
- Compact_Lie_algebra sameAs m.09gb8v8.
- Compact_Lie_algebra sameAs Q5155287.
- Compact_Lie_algebra sameAs Q5155287.
- Compact_Lie_algebra wasDerivedFrom Compact_Lie_algebra?oldid=582094399.
- Compact_Lie_algebra isPrimaryTopicOf Compact_Lie_algebra.