If h is an ideal of the Lie algebra g and h is also a subalgebra of k, then the GeneralizedCenter(h, k) is the ideal of vectors x in k such that [x,y] in h for all y in k.  In particular, the generalized center of h in g is the inverse image of the center of the quotient algebra g/h with respect to the canonical projection map g -> g/h.

A list of vectors defining a basis for the generalized center of h in k is returned.  If the optional argument S2 is omitted, then the default is k = g.

If the generalized center of h in k is trivial, then an empty list is returned.

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