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- F4_(mathematics) abstract "In mathematics, F4 is the name of a Lie group and also its Lie algebra f4. It is one of the five exceptional simple Lie groups. F4 has rank 4 and dimension 52. The compact form is simply connected and its outer automorphism group is the trivial group. Its fundamental representation is 26-dimensional.The compact real form of F4 is the isometry group of a 16-dimensional Riemannian manifold known as the octonionic projective plane OP2. This can be seen systematically using a construction known as the magic square, due to Hans Freudenthal and Jacques Tits.There are 3 real forms: a compact one, a split one, and a third one. They are the isometry groups of the three real Albert algebras.The F4 Lie algebra may be constructed by adding 16 generators transforming as a spinor to the 36-dimensional Lie algebra so(9), in analogy with the construction of E8.In older books and papers, F4 is sometimes denoted by E4.".
- F4_(mathematics) thumbnail Dynkin_diagram_F4.png?width=300.
- F4_(mathematics) wikiPageExternalLink books?isbn=0226005275.
- F4_(mathematics) wikiPageExternalLink node15.html..
- F4_(mathematics) wikiPageExternalLink home.html.
- F4_(mathematics) wikiPageID "292877".
- F4_(mathematics) wikiPageLength "6568".
- F4_(mathematics) wikiPageOutDegree "50".
- F4_(mathematics) wikiPageRevisionID "664720332".
- F4_(mathematics) wikiPageWikiLink 24-cell.
- F4_(mathematics) wikiPageWikiLink Adjoint_representation_of_a_Lie_algebra.
- F4_(mathematics) wikiPageWikiLink Albert_algebra.
- F4_(mathematics) wikiPageWikiLink Body-centered_cubic.
- F4_(mathematics) wikiPageWikiLink Category:Algebraic_groups.
- F4_(mathematics) wikiPageWikiLink Category:Lie_groups.
- F4_(mathematics) wikiPageWikiLink Cayley_plane.
- F4_(mathematics) wikiPageWikiLink Coxeter_group.
- F4_(mathematics) wikiPageWikiLink Cubic_crystal_system.
- F4_(mathematics) wikiPageWikiLink Dynkin_diagram.
- F4_(mathematics) wikiPageWikiLink E8_(mathematics).
- F4_(mathematics) wikiPageWikiLink File:Dynkin_diagram_F4.png.
- F4_(mathematics) wikiPageWikiLink Freudenthal_magic_square.
- F4_(mathematics) wikiPageWikiLink Fundamental_representation.
- F4_(mathematics) wikiPageWikiLink Hans_Freudenthal.
- F4_(mathematics) wikiPageWikiLink Hermitian_matrix.
- F4_(mathematics) wikiPageWikiLink Hurwitz_quaternion.
- F4_(mathematics) wikiPageWikiLink Hypercubic_honeycomb.
- F4_(mathematics) wikiPageWikiLink Hypercubic_lattice.
- F4_(mathematics) wikiPageWikiLink Isometry_group.
- F4_(mathematics) wikiPageWikiLink Jacques_Tits.
- F4_(mathematics) wikiPageWikiLink John_Baez.
- F4_(mathematics) wikiPageWikiLink John_C._Baez.
- F4_(mathematics) wikiPageWikiLink Lattice_(group).
- F4_(mathematics) wikiPageWikiLink Lie_algebra.
- F4_(mathematics) wikiPageWikiLink Lie_group.
- F4_(mathematics) wikiPageWikiLink List_of_simple_Lie_groups.
- F4_(mathematics) wikiPageWikiLink Mathematics.
- F4_(mathematics) wikiPageWikiLink Matrix_(mathematics).
- F4_(mathematics) wikiPageWikiLink Octonion.
- F4_(mathematics) wikiPageWikiLink Octonionic_projective_plane.
- F4_(mathematics) wikiPageWikiLink Outer_automorphism_group.
- F4_(mathematics) wikiPageWikiLink Riemannian_manifold.
- F4_(mathematics) wikiPageWikiLink Ring_(mathematics).
- F4_(mathematics) wikiPageWikiLink Root_system.
- F4_(mathematics) wikiPageWikiLink Simple_Lie_group.
- F4_(mathematics) wikiPageWikiLink Simple_root_(root_system).
- F4_(mathematics) wikiPageWikiLink Solvable_group.
- F4_(mathematics) wikiPageWikiLink Spinor.
- F4_(mathematics) wikiPageWikiLink Symmetry_group.
- F4_(mathematics) wikiPageWikiLink Trivial_group.
- F4_(mathematics) wikiPageWikiLink University_of_Chicago_Press.
- F4_(mathematics) wikiPageWikiLink Weyl_character_formula.
- F4_(mathematics) wikiPageWikiLink Weyl_group.
- F4_(mathematics) wikiPageWikiLink File:F4HassePoset.svg.
- F4_(mathematics) wikiPageWikiLink File:F4_roots_by_24-cell_duals.svg.
- F4_(mathematics) wikiPageWikiLinkText "".
- F4_(mathematics) wikiPageWikiLinkText "F4 (mathematics)".
- F4_(mathematics) wikiPageWikiLinkText "F4".
- F4_(mathematics) wikiPageWikiLinkText "F4_(mathematics)#F4_lattice".
- F4_(mathematics) wikiPageWikiLinkText "coloured in 2 colours".
- F4_(mathematics) hasPhotoCollection F4_(mathematics).
- F4_(mathematics) wikiPageUsesTemplate Template:CDD.
- F4_(mathematics) wikiPageUsesTemplate Template:Citation.
- F4_(mathematics) wikiPageUsesTemplate Template:Cite_book.
- F4_(mathematics) wikiPageUsesTemplate Template:Cite_journal.
- F4_(mathematics) wikiPageUsesTemplate Template:Dynkin2.
- F4_(mathematics) wikiPageUsesTemplate Template:Exceptional_Lie_groups.
- F4_(mathematics) wikiPageUsesTemplate Template:Group_theory_sidebar.
- F4_(mathematics) wikiPageUsesTemplate Template:Lie_groups.
- F4_(mathematics) wikiPageUsesTemplate Template:OEIS.
- F4_(mathematics) subject Category:Algebraic_groups.
- F4_(mathematics) subject Category:Lie_groups.
- F4_(mathematics) hypernym Group.
- F4_(mathematics) type Band.
- F4_(mathematics) comment "In mathematics, F4 is the name of a Lie group and also its Lie algebra f4. It is one of the five exceptional simple Lie groups. F4 has rank 4 and dimension 52. The compact form is simply connected and its outer automorphism group is the trivial group. Its fundamental representation is 26-dimensional.The compact real form of F4 is the isometry group of a 16-dimensional Riemannian manifold known as the octonionic projective plane OP2.".
- F4_(mathematics) label "F4 (mathematics)".
- F4_(mathematics) sameAs F4,_матэматыка.
- F4_(mathematics) sameAs F4_(mathématiques).
- F4_(mathematics) sameAs F₄.
- F4_(mathematics) sameAs m.01qtnk.
- F4_(mathematics) sameAs F4_(математика).
- F4_(mathematics) sameAs Q869077.
- F4_(mathematics) sameAs Q869077.
- F4_(mathematics) wasDerivedFrom F4_(mathematics)?oldid=664720332.
- F4_(mathematics) depiction Dynkin_diagram_F4.png.
- F4_(mathematics) isPrimaryTopicOf F4_(mathematics).