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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:class
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Classification involves Dynkin diagrams
Classification involves root systems
Classified over algebraically closed fields
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gptkbp:defines
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Groups that are also algebraic varieties such that the group operations are given by regular maps
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gptkbp:example
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gptkb:Torus
gptkb:Special_linear_group
gptkb:Additive_group
gptkb:Multiplicative_group
Abelian variety
Elliptic curve
General linear group
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gptkbp:field
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gptkb:Algebraic_geometry
gptkb:Abstract_algebra
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gptkbp:hasApplication
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gptkb:Algebraic_topology
gptkb:Langlands_program
gptkb:Representation_theory
gptkb:Automorphic_forms
gptkb:Algebraic_number_theory
gptkb:Quantum_groups
Cryptography
Coding theory
Moduli spaces
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gptkbp:hasProperty
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Group operation is a morphism of varieties
Inverse operation is a morphism of varieties
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gptkbp:hasSubfield
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gptkb:Torus
gptkb:Reductive_group
gptkb:Unipotent_group
gptkb:Linear_algebraic_group
gptkb:Nilpotent_group
gptkb:Parabolic_subgroup
gptkb:Semisimple_group
gptkb:Solvable_group
Abelian variety
Borel subgroup
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https://www.w3.org/2000/01/rdf-schema#label
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Algebraic groups
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gptkbp:importantFor
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gptkb:Number_theory
gptkb:Algebraic_geometry
gptkb:Representation_theory
Arithmetic geometry
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gptkbp:relatedTo
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gptkb:Lie_groups
gptkb:Affine_algebraic_group
gptkb:Algebraic_torus
gptkb:Reductive_group
gptkb:Linear_algebraic_group
Abelian group
Algebraic group scheme
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gptkbp:studiedBy
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gptkb:André_Weil
gptkb:Claude_Chevalley
gptkb:Jean-Pierre_Serre
gptkb:Armand_Borel
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gptkbp:studiedIn
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gptkb:Group_theory
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gptkbp:subclassOf
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gptkb:algebraic_geometry
gptkb:group_of_people
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gptkbp:bfsParent
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gptkb:Topological_Groups
gptkb:Simple_Singularities_and_Simple_Algebraic_Groups
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gptkbp:bfsLayer
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6
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