A bracket operation [ , ] on a vector space g defines a Lie bracket if it is bi-linear, skewsymmetric, and satisfies [[x, y], z] + [[z, x], y] + [[y, z], x] = 0.

In terms of the standard exterior derivative operator d defined on the exterior algebra of the dual space g* (defined on 1-forms by d(x, y) = - [x, y]), the Jacobi identities are equivalent to d^2 = 0.

The program DGsetup does not check that its input, a Lie algebra data structure, actually defines a Lie algebra.  To verify that a Lie algebra data structure does indeed define a Lie algebra, initialize the Lie algebra data structure, and run Query("Jacobi").

Query(Alg, "Jacobi") returns true if the Jacobi identities hold (in which case Alg defines a Lie algebra) and false otherwise.  If the algebra is unspecified, then LieAlgebraCheck is applied to the current algebra.

Query(Alg, parm, "Jacobi") returns a sequence TF, Eq, Soln, AlgList.  Here TF is true if Maple finds parameter values for which the Jacobi identities are valid and false otherwise; Eq is the set of equations (with the variables parm as unknowns) which must be satisfied for the Jacobi identities to hold; Soln is the list of solutions to the equations Eq; and AlgList is the list of Lie algebra data structures obtained from the parameter values given by various solutions in Soln.

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