Example 1.

First we obtain a Lie algebra of vector fields from the paper by Gonzalez-Lopez, Kamran, Olver in the DifferentialGeometry Library using the Retrieve command and then we compute the isotropy filtration.

We calculate the isotropy filtration as a subalgebra of Gamma.

We calculate the isotropy filtration as a subalgebra of the abstract Lie algebra defined by Gamma. To this end, we first calculate the structure constants for Gamma and initialize the result as Alg1.

Re-run the IsotropyFiltration command with the 3rd argument output = [Alg1].

We check that F does indeed define a filtration (note that there is an index shift Gamma^k_p = F[k + 1]).

All these brackets can be checked at once with Query/"filtration".

DifferentialGeometry, GroupActions, Library, LieAlgebras, BracketOfSubspaces, IsotropySubalgebra, LieAlgebraData, Query