Linear Algebraic Groups

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

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:mathematical_concept
gptkbp:application	gptkb:Physics gptkb:Number_theory gptkb:Algebraic_geometry gptkb:Representation_theory
gptkbp:category	gptkb:Algebraic_geometry gptkb:Group_theory gptkb:Linear_algebra gptkb:Algebraic_groups
gptkbp:defines	Group that is also an algebraic variety such that the group operations are given by regular functions
gptkbp:example	gptkb:Orthogonal_group gptkb:Special_linear_group gptkb:Symplectic_group gptkb:Unitary_group General linear group
gptkbp:field	gptkb:Algebraic_geometry gptkb:Group_theory gptkb:Linear_algebra
https://www.w3.org/2000/01/rdf-schema#label	Linear Algebraic Groups
gptkbp:notableBook	gptkb:Linear_Algebraic_Groups_by_Armand_Borel gptkb:Linear_Algebraic_Groups_by_James_E._Humphreys
gptkbp:property	Can be connected or disconnected Can be defined over arbitrary fields Can be reductive, semisimple, or solvable
gptkbp:relatedConcept	gptkb:Weyl_group gptkb:Lie_group gptkb:Affine_algebraic_group gptkb:Algebraic_torus gptkb:Reductive_group gptkb:Root_system gptkb:Torus_(algebraic_group) gptkb:Unipotent_group Borel subgroup Group scheme
gptkbp:studiedBy	gptkb:Claude_Chevalley gptkb:Robert_Steinberg gptkb:Armand_Borel
gptkbp:subclassOf	gptkb:Lie_group
gptkbp:bfsParent	gptkb:James_E._Humphreys
gptkbp:bfsLayer	6