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LieAlgebras

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find the ad Matrix for a vector in a Lie algebra

find the structure equations for a real algebra defined by a list of matrices and a multiplication procedure

DifferentialGeometry/LieAlgebras/AlgebraLibraryData
retrieve the structure equations for various classical algebras (quaternions, octonions, Clifford algebras, and low dimensional Jordan algebras)

DifferentialGeometry/LieAlgebras/AlgebraNorm
find the norm of a quaternion or octonion

DifferentialGeometry/LieAlgebras/ApplyHomomorphism
apply a Lie algebra homomorphism to a vector, form or tensor

DifferentialGeometry/LieAlgebras/AscendingIdealsBasis
find a basis for a solvable Lie algebra which defines an ascending chain of ideals

DifferentialGeometry/LieAlgebras/BracketOfSubspaces
calculate the span of the Lie bracket of two lists of vectors in a Lie algebra, calculate the span of the matrix commutator of two lists of matrices

DifferentialGeometry/LieAlgebras/CartanDecomposition
find a Cartan decomposition of a non-compact semi-simple Lie algebra

DifferentialGeometry/LieAlgebras/CartanMatricesDetails
Details for Cartan matrices and Dynkin diagrams

DifferentialGeometry/LieAlgebras/CartanMatrix
find the Cartan matrix for a simple Lie algebra from a root space decomposition, display the Cartan matrix for a given root type

DifferentialGeometry/LieAlgebras/CartanMatrixToStandardForm
transform a Cartan matrix to standard form

DifferentialGeometry/LieAlgebras/CartanSubalgebra
find a Cartan subalgebra of a Lie algebra

DifferentialGeometry/LieAlgebras/Center
find the center of a Lie algebra or a non-commutative algebra

DifferentialGeometry/LieAlgebras/Centralizer
find the centralizer of a list of vectors

change one or more components of a graded Lie algebra

DifferentialGeometry/LieAlgebras/ChangeLieAlgebraTo
change the current frame to the frame for a Lie algebra

DifferentialGeometry/LieAlgebras/ChangeRepresentationBasis
change the basis for a representation, either in the Lie algebra or in the representation space

DifferentialGeometry/LieAlgebras/ChevalleyBasis
find the Chevalley basis for a real, split semi-simple Lie algebra

DifferentialGeometry/LieAlgebras/CoRoot
find the coroot of a root vector for a semi-simple Lie algebra

DifferentialGeometry/LieAlgebras/Codifferential
calculate the codifferential of a multi-vector defined on a Lie algebra with coefficients in a representation

DifferentialGeometry/LieAlgebras/Cohomology
compute relative Lie algebra cohomology with coefficients in a representation

DifferentialGeometry/LieAlgebras/CompactRoots
find the compact roots in a root system for a non-compact semi-simple real Lie algebra

DifferentialGeometry/LieAlgebras/Complexify
LieAlgebras[Complexify] find the complexification of a Lie algebra

DifferentialGeometry/LieAlgebras/Decompose
decompose a Lie algebra into a direct sum of indecomposable Lie algebras

DifferentialGeometry/LieAlgebras/Deformation
find the deformation of a Lie algebra defined by a list of 2-forms

DifferentialGeometry/LieAlgebras/Derivations
find the derivations of a Lie algebra, find the derivations of a general non-commutative algebra

DifferentialGeometry/LieAlgebras/DerivedAlgebra
find the derived algebra of a Lie algebra

DifferentialGeometry/LieAlgebras/DirectSum
create the direct sum of a list of Lie algebras

DifferentialGeometry/LieAlgebras/DirectSumOfRepresentations
form the direct sum representation for a list of representations of a Lie algebra

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