Example 1.
We use the Retrieve command to obtain a Lie algebra of vector fields in the paper by Gonzalez-Lopez, Kamran, and Olver from the DifferentialGeometry Library. We compute the isotropy subalgebra and isotropy representation at the points and
We illustrate some different possible outputs from the IsotropySubalgebra program.
Note that the vectors in Iso2 all vanish at
It is apparent from the multiplication table that the pair Alg1, S1 is a symmetric pair with respect to the complementary subspace. We can check this with the command Query/"SymmetricPair".
The linear isotropy representation can be converted to a representation.