F4 (Lie algebra)

URI: https://gptkb.org/entity/F4_(Lie_algebra)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Lie_group
gptkbp:automorphismGroup	F4 (group)
gptkbp:Cartan_matrix	F4 Cartan matrix
gptkbp:compact_real_form	yes
gptkbp:dimensions	52
gptkbp:discoveredBy	gptkb:Élie_Cartan
gptkbp:Dynkin_diagram	gptkb:F4_diagram
gptkbp:has_24_long_roots	yes
gptkbp:has_24_short_roots	yes
gptkbp:has_48_roots	yes
gptkbp:has_compact_real_form	yes
gptkbp:has_complex_form	yes
gptkbp:has_root_lattice	F4 lattice
gptkbp:has_split_real_form	yes
https://www.w3.org/2000/01/rdf-schema#label	F4 (Lie algebra)
gptkbp:is_a_subalgebra_of	E6 (Lie algebra) E7 (Lie algebra) E8 (Lie algebra)
gptkbp:rank	4
gptkbp:realForm	3
gptkbp:relatedGroup	F4 (group)
gptkbp:relatedTo	gptkb:Albert_algebra gptkb:exceptional_Jordan_algebra gptkb:exceptional_Lie_groups gptkb:octonions
gptkbp:split_real_form	yes
gptkbp:type	gptkb:exceptional_Lie_algebra gptkb:F4_root_system
gptkbp:used_in	theory of Lie groups theory of Lie algebras theory of algebraic groups
gptkbp:Weyl_group	1152
gptkbp:bfsParent	gptkb:F4(q)
gptkbp:bfsLayer	6