The isotropy subalgebra Gamma_p of a Lie algebra of vector fields Gamma at the point p is defined by Gamma_p = {X in Gamma | X_p = 0}.  The Lie bracket defines a natural representation rho of Gamma_p on the tangent space T_pM by rho(X)(Y) = [X, Y], where X in Gamma_p and Y in T_pM.

IsotropySubalgebra returns a list of vectors giving the isotropy subalgebra Gamma_p as a subalgebra of Gamma.

With output = ["Vector", "Representation"], two lists are returned.  The first is a list of vectors giving the isotropy subalgebra Gamma_p as a subalgebra of Gamma and the second is the list of matrices defining the linear isotropy representation with respect to the standard basis for T_pM.

Let algname be the name of the abstract Lie algebra g created from Gamma.  With output = ["Vector", algname], the second list returned gives the isotropy subalgebra as a subalgebra of the abstract Lie algebra g.

The command IsotropySubalgebra is part of the DifferentialGeometry:-GroupActions package.  It can be used in the form IsotropySubalgebra(...) only after executing the commands with(DifferentialGeometry) and with(GroupActions), but can always be used by executing DifferentialGeometry:-GroupActions:-IsotropySubalgebra(...).