F4 Lie group

URI: https://gptkb.org/entity/F4_Lie_group

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Lie_group
gptkbp:associatedWith	gptkb:Albert_algebra gptkb:octonions
gptkbp:automorphismGroup	trivial
gptkbp:centralTo	trivial
gptkbp:compact_real_form	F4 (compact)
gptkbp:complexification	F4(C)
gptkbp:dimensions	52
gptkbp:discoveredBy	gptkb:Élie_Cartan
gptkbp:Dynkin_diagram	gptkb:F4
gptkbp:first_classified	1900s
gptkbp:fundamentalGroup	trivial
gptkbp:has_Weyl_group	gptkb:Weyl_group_of_F4
https://www.w3.org/2000/01/rdf-schema#label	F4 Lie group
gptkbp:rank	4
gptkbp:realForm	3
gptkbp:related_algebra	gptkb:F4_Lie_algebra
gptkbp:relatedTo	gptkb:Weyl_group gptkb:E7_Lie_group gptkb:Spin(8) gptkb:Moufang_plane gptkb:exceptional_Jordan_algebra gptkb:exceptional_Lie_groups gptkb:Freudenthal_magic_square gptkb:exceptional_Lie_algebras gptkb:Tits_group gptkb:E8_Lie_group gptkb:G2_Lie_group gptkb:Spin(9) gptkb:E6_Lie_group gptkb:Riemannian_symmetric_spaces exceptional holonomy exceptional geometry exceptional structures in mathematics Borel–de Siebenthal theory Albert algebra automorphism group projective geometry over octonions
gptkbp:split_real_form	F4(4)
gptkbp:type	gptkb:Lie_group gptkb:F4_root_system
gptkbp:used_in	gptkb:string_theory grand unified theories theory of Lie algebras theory of algebraic groups theory of algebraic geometry theory of particle physics
gptkbp:Weyl_group	1152
gptkbp:bfsParent	gptkb:G2_Lie_group
gptkbp:bfsLayer	7