Statements (56)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:musical_group
|
| gptkbp:are_a_special_case_of |
group schemes
|
| gptkbp:are_classified_by |
their rank
|
| gptkbp:are_defined_over |
finite fields
|
| gptkbp:can_be_defined_over |
arbitrary fields
|
| gptkbp:can_be_defined_using |
Chevalley generators
Chevalley relations |
| gptkbp:can_be_realized_as |
projective varieties
|
| gptkbp:can_be_used_in |
theory of modular forms
|
| gptkbp:constructed_in |
Lie algebras
algebraic varieties Tits systems homogeneous vector bundles other algebraic structures |
| gptkbp:contains |
gptkb:SL(n,_q)
gptkb:SO(n,_q) gptkb:Sp(2n,_q) |
| gptkbp:example |
simple groups
connected algebraic groups linear groups |
| gptkbp:has_applications_in |
number theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Chevalley groups
|
| gptkbp:is_associated_with |
root systems
|
| gptkbp:is_connected_to |
Galois cohomology
the Langlands program Lie theory the theory of group actions |
| gptkbp:is_described_as |
Galois representations
|
| gptkbp:is_essential_for |
theory of algebraic groups
the study of symmetry the study of algebraic geometry the study of algebraic topology |
| gptkbp:is_related_to |
algebraic topology
automorphism groups semisimple groups the theory of algebraic groups over local fields the theory of algebraic cycles |
| gptkbp:is_represented_in |
matrix groups
algebraic varieties over finite fields characteristic zero |
| gptkbp:is_studied_for |
moduli spaces
homogeneous spaces cohomological dimensions the structure of algebraic groups. |
| gptkbp:is_studied_in |
algebraic geometry
modular representations representation categories the theory of algebraic stacks |
| gptkbp:is_used_in |
gptkb:crypt
representation theory |
| gptkbp:named_after |
gptkb:Claude_Chevalley
|
| gptkbp:scientific_classification |
gptkb:Dynkin_diagrams
their root data |
| gptkbp:type_of |
linear algebraic group
|
| gptkbp:bfsParent |
gptkb:Claude_Chevalley
|
| gptkbp:bfsLayer |
6
|