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gptkbp:instanceOf
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gptkb:algebra
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gptkbp:basisFor
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gptkb:root
gptkb:Chevalley_basis
Cartan subalgebra
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gptkbp:class
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gptkb:Cartan_classification
gptkb:Dynkin_diagrams
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gptkbp:definedIn
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gptkb:Field
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gptkbp:example
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gptkb:Witt_algebra
gptkb:Virasoro_algebra
gptkb:Lie_group
gptkb:Heisenberg_algebra
nilpotent Lie algebra
semisimple Lie algebra
solvable Lie algebra
matrix Lie algebra
abelian Lie algebra
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gptkbp:field
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gptkb:Lie_theory
abstract algebra
differential geometry
representation theory
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gptkbp:generalizes
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associative algebras
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gptkbp:namedAfter
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gptkb:Sophus_Lie
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gptkbp:operator
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Lie bracket
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gptkbp:property
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Jacobi identity
alternativity
bilinearity
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gptkbp:relatedConcept
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gptkb:Weyl_algebra
gptkb:Weyl_group
gptkb:model
gptkb:complex_Lie_algebra
gptkb:infinite-dimensional_Lie_algebra
gptkb:real_Lie_algebra
gptkb:weight_lattice
gptkb:isomorphism
gptkb:Borel_subalgebra
gptkb:Casimir_operator
gptkb:Killing_form
gptkb:Lie_algebra_cohomology
gptkb:Ado's_theorem
gptkb:Cartan–Weyl_basis
gptkb:Engel's_theorem
gptkb:Jordan–Chevalley_decomposition
gptkb:Kac–Moody_algebra
gptkb:Killing–Cartan_classification
gptkb:Levi_decomposition
gptkb:Lie's_theorem
gptkb:Poincaré–Birkhoff–Witt_theorem
gptkb:Serre_relations
gptkb:Whitehead's_lemma
gptkb:classical_Lie_algebra
gptkb:exceptional_Lie_algebra
gptkb:orthogonal_Lie_algebra
gptkb:special_linear_Lie_algebra
gptkb:special_orthogonal_Lie_algebra
gptkb:special_unitary_Lie_algebra
gptkb:super_Lie_algebra
gptkb:symplectic_Lie_algebra
gptkb:unitary_Lie_algebra
gptkb:universal_enveloping_algebra
gptkb:ideal
representation theory
center of a Lie algebra
homomorphism
representation ring
structure constants
structure theory
highest weight
derivation
enveloping algebra
automorphism group
compact Lie algebra
finite-dimensional Lie algebra
non-compact Lie algebra
reductive Lie algebra
root space decomposition
root system classification
simple root
split Lie algebra
subalgebra
weight space
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gptkbp:relatedTo
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gptkb:Lie_groups
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gptkbp:represents
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adjoint representation
fundamental representation
highest weight representation
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gptkbp:studiedIn
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gptkb:mathematics
gptkb:theoretical_physics
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gptkbp:usedIn
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gptkb:partial_differential_equations
particle physics
quantum mechanics
symmetry analysis
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gptkbp:bfsParent
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gptkb:Lie_theory
gptkb:Wilhelm_Magnus
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gptkbp:bfsLayer
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5
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https://www.w3.org/2000/01/rdf-schema#label
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Lie algebras
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