|
gptkbp:instanceOf
|
gptkb:algebraic_geometry
gptkb:group_of_people
|
|
gptkbp:builtBy
|
gptkb:Chevalley_basis
|
|
gptkbp:definedIn
|
arbitrary field
|
|
gptkbp:example
|
gptkb:exceptional_groups_of_Lie_type
gptkb:special_linear_group_SL(n,q)
gptkb:special_orthogonal_group_SO(n,q)
gptkb:symplectic_group_Sp(2n,q)
|
|
gptkbp:fieldOfStudy
|
gptkb:algebra
group theory
finite group theory
|
|
gptkbp:hasFiniteVersion
|
gptkb:finite_Chevalley_group
|
|
gptkbp:hasInfiniteVersion
|
gptkb:infinite_Chevalley_group
|
|
gptkbp:hasProperty
|
important in classification of finite simple groups
arise from Dynkin diagrams
arise from Lie algebras
arise from Lie algebras of semisimple type
arise from root systems
can be defined over any field
can be defined over finite fields
can be defined over infinite fields
can be twisted or untwisted
constructed using Chevalley basis
include classical groups
include exceptional groups
many are simple groups
used in algebraic group theory
used in finite group theory
|
|
gptkbp:hasType
|
gptkb:twisted_group_of_Lie_type
gptkb:untwisted_group_of_Lie_type
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Chevalley groups
|
|
gptkbp:introduced
|
gptkb:Claude_Chevalley
|
|
gptkbp:introducedIn
|
1955
|
|
gptkbp:namedAfter
|
gptkb:Claude_Chevalley
|
|
gptkbp:partOf
|
gptkb:groups_of_Lie_type
|
|
gptkbp:relatedTo
|
gptkb:Weyl_group
gptkb:algebraic_geometry
gptkb:group_of_people
gptkb:Lie_group
gptkb:root
gptkb:Steinberg_group
gptkb:Tits_group
algebraic group over finite field
reductive group
semisimple group
|
|
gptkbp:subclassOf
|
gptkb:Lie_group
simple group
|
|
gptkbp:usedIn
|
classification of finite simple groups
|
|
gptkbp:bfsParent
|
gptkb:Weyl_group
|
|
gptkbp:bfsLayer
|
5
|