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Query

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DifferentialGeometry/LieAlgebras/Query/Abelian
check if a Lie algebra is Abelian

DifferentialGeometry/LieAlgebras/Query/Derivation
check if a matrix defines a derivation on a Lie algebra

DifferentialGeometry/LieAlgebras/Query/DirectSumDecomposition
check if a list of subalgebras defines a direct sum decomposition of a Lie algebra

DifferentialGeometry/LieAlgebras/Query/Filtration
check if a list of subspaces defines a decreasing filtration of a Lie algebra

DifferentialGeometry/LieAlgebras/Query/Gradation
check if a list of subspaces defines a gradation of a Lie algebra

DifferentialGeometry/LieAlgebras/Query/Homomorphism
check if a matrix defines a Lie algebra homomorphism between two Lie algebras

DifferentialGeometry/LieAlgebras/Query/Indecomposable
check if a Lie algebra is decomposable as a direct sum of Lie algebras over the real numbers

DifferentialGeometry/LieAlgebras/Query/Jacobi
check if a list of structure equations defines a Lie algebra by verifying the Jacobi identities

DifferentialGeometry/LieAlgebras/Query/Keywords
list the admissible keywords for the procedure Query

DifferentialGeometry/LieAlgebras/Query/LeviDecomposition
check that a pair of subalgebras define a Levi decomposition of a Lie algebra

DifferentialGeometry/LieAlgebras/Query/NaturallyReductivePair
check if a subalgebra, subspace pair is naturally reductive with respect to an inner product on the subspace

DifferentialGeometry/LieAlgebras/Query/Nilpotent
check if a Lie algebra is nilpotent

DifferentialGeometry/LieAlgebras/Query/ReductivePair
check if a subalgebra, subspace pair defines a reductive pair in a Lie algebra

DifferentialGeometry/LieAlgebras/Query/Semisimple
check if a Lie algebra is semisimple

DifferentialGeometry/LieAlgebras/Query/Solvable
check if a Lie algebra is solvable

DifferentialGeometry/LieAlgebras/Query/Subalgebra
check if a list of vectors defines a Lie subalgebra

DifferentialGeometry/LieAlgebras/Query/SymmetricPair
check if a subalgebra, subspace pair defines a symmetric pair in a Lie algebra


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