FormStructureEquations   LieAlgebraName  MatrixAlgebra 
StructureConstants       Subalgebra      VectorFields  
VectorStructureEquations                                

Example 1.  LieAlgebraData(StructureConstants)

In this example we create a 3 dimensional Array, C, of structure constants and use this Array to create a Lie algebra data structure for a Lie algebra called Ex1.

Example 2.  LieAlgebraData(VectorStructureEquations)

In this example we create a Lie algebra data structure for a Lie algebra called Ex2 from a list of structure equations for the Lie brackets.

Example 3.  LieAlgebraData(FormStructureEquations)

In this example we create a Lie algebra data structure for a Lie algebra called Ex3 from a list of structure equations for the exterior derivatives of the dual 1-forms.

Example 4.  LieAlgebraData(MatrixAlgebra)

In this example we create a Lie algebra data structure for a Lie algebra called Ex4 from a list of matrices.

Example 5.  LieAlgebraData(LieAlgebraName)

In this example we create a Lie algebra data structure for a Lie algebra called Ex5 from a previously initialized Lie algebra.

First we initialize a Lie algebra Ex5.

Applying LieAlgebraData to Ex5 gives back the Lie algebra data structure we started from.

Example 6.  LieAlgebraData(Subalgebra, "LieAlgebraData")

In this example we create a Lie algebra data structure from a subalgebra of a Lie algebra.

First we initialize a Lie algebra Alg5.

The vectors [e1, e2, e3] define a Lie subalgebra which we wish to initialize as a Lie algebra in its own right.

DifferentialGeometry, LieAlgebras, Query