exceptional Lie group G 2

URI: https://gptkb.org/entity/exceptional_Lie_group_G_2

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Lie_group
gptkbp:automorphismGroup	gptkb:octonions
gptkbp:Cartan_matrix	[[2,-3],[-1,2]]
gptkbp:centralTo	trivial
gptkbp:compact_real_form	gptkb:G_2
gptkbp:complexification	G_2(C)
gptkbp:dimensions	14
gptkbp:discoveredBy	gptkb:Wilhelm_Killing
gptkbp:discoveredIn	1887
gptkbp:Dynkin_diagram	two nodes connected by a triple bond
gptkbp:fundamentalGroup	trivial
https://www.w3.org/2000/01/rdf-schema#label	exceptional Lie group G 2
gptkbp:isTransitiveOn	6-sphere S^6
gptkbp:Lie_algebra	g_2
gptkbp:maximal_compact_subgroup_of	G_2(2)
gptkbp:number_of_positive_roots	6
gptkbp:number_of_simple_roots	2
gptkbp:rank	2
gptkbp:realForm	compact form split form
gptkbp:relatedTo	gptkb:E_6 gptkb:E_7 gptkb:E_8 gptkb:string_theory gptkb:SU(3) gptkb:exceptional_Jordan_algebra gptkb:SO(7) gptkb:Spin(7) gptkb:M-theory gptkb:octonions differential geometry representation theory F_4 exceptional holonomy special holonomy manifolds subgroup of SO(7) G_2 manifold exceptional Lie algebra g_2
gptkbp:split_real_form	G_2(2)
gptkbp:type	gptkb:G_2_root_system
gptkbp:used_in	differential geometry theory of special holonomy string theory compactifications
gptkbp:Weyl_group	gptkb:dihedral_group_of_order_12 12
gptkbp:bfsParent	gptkb:G_2_Lie_algebra
gptkbp:bfsLayer	8