E 7 Lie algebra

URI: https://gptkb.org/entity/E_7_Lie_algebra

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Lie_group
gptkbp:adjointRepresentationDimension	133
gptkbp:automorphismGroup	gptkb:E_7_adjoint_group
gptkbp:Cartan_matrix	gptkb:E_7_Cartan_matrix
gptkbp:centralTo	trivial
gptkbp:dimensions	133
gptkbp:discoveredBy	gptkb:Wilhelm_Killing gptkb:Élie_Cartan
gptkbp:Dynkin_diagram	gptkb:E_7_Dynkin_diagram
gptkbp:firstClassified	late 19th century
gptkbp:fundamentalRepresentationDimension	56
gptkbp:rank	7 complex numbers
gptkbp:realForm	gptkb:E_{7(-133)} gptkb:E_{7(-25)} gptkb:E_{7(-5)} gptkb:E_{7(7)}
gptkbp:relatedGroup	gptkb:E_7_Lie_group
gptkbp:relatedTo	gptkb:E_6_Lie_algebra gptkb:exceptional_Jordan_algebra gptkb:E_8_Lie_algebra gptkb:Freudenthal_magic_square gptkb:octonions
gptkbp:type	gptkb:Lie_group gptkb:E_7_root_system gptkb:exceptional_Lie_algebra
gptkbp:usedIn	gptkb:theoretical_physics gptkb:string_theory grand unified theories
gptkbp:Weyl_group	2903040
gptkbp:bfsParent	gptkb:E_{7(-133)} gptkb:E_7_Cartan_matrix gptkb:E_7_root_system gptkb:E_7^{(1)}
gptkbp:bfsLayer	9
https://www.w3.org/2000/01/rdf-schema#label	E 7 Lie algebra