A matrix A is a derivation for g if the associated linear transformation mapping g to g satisfies A([x, y]) = [A(x), y] + [x, A(y)] for all x, y in g.  The set of all derivations defines a matrix Lie algebra Derivations(g).  For each x in g the matrix A= ad(x) defines a derivation -- these are the inner derivations Derivations(g, "Inner").  The inner derivations define an ideal in Derivations(g) and the quotient Lie algebra Derivations(g)/Derivations(g, "Inner") is the Lie algebra of outer derivations.

Derivations(Algname, "Inner") returns a list of linearly independent matrices which defines a basis for the Lie algebra of inner derivations for the Lie algebra Algname.

Derivations(Algname, "Full") returns a list of linearly independent matrices which defines a basis for the Lie algebra of all derivations for the Lie algebra Algname.

Derivations(Algname, "Outer") returns a list of linearly independent matrices which gives a representative list of the outer derivations for the Lie algebra Algname.

If the first (optional) argument Algname is missing, then the derivations of the current Lie algebra are computed.

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