Example 1.
We illustrate the first calling sequence for LieAlgebraData using the Lie algebra and a 5-step gradation (Grading of semi-simple Lie algebras are easily constructed with GradedSemiSimpleLieAlgebra ). Use SimpleLieAlgebraData and DGsetup to initialize .
Here is the grading we shall use.
Here are the structure equations for adapted to the basis .
We see that the grading weights are increasing in this new basis.
With the keyword argument order = decreasing we obtain:
Now the grading weights are decreasing in the new basis.
With the second calling sequence we can, for example, also obtain the structure equations for just the negatively graded components of.
We see that the negatively graded components give the subalgebra:
with structure equations: