The Poisson brackets of D with itself depend on the sign of H, i.e., on whether the energy is negative (producing closed, elliptical orbits under an inverse-square central force) or positive (producing open, hyperbolic orbits under an inverse-square central force). For negative energies—i.e., for bound systems—the Poisson brackets are { D i , D j } = ∑ ∑ s = 1 3 ε ε i j s L s . We may now appreciate the motivation for the chosen scaling of D : With this scaling, the Hamiltonian no longer appears on the right-hand side of the preceding relation. Thus, the span of the three components of L and the three components of D forms a six-dimensional Lie algebra under the Poisson bracket. This Lie algebra is isomorphic to so(4), the Lie algebra of the 4-dimensional rotation group SO(4).