Gravitational constraints that generate a Lie algebra

The coupling of gravity to dust helps one discover simple quadratic combinations of the gravitational super-Hamiltonian and supermomentum whose Poisson brackets strongly vanish. This leads to a new form of vacuum constraints which generate a true Lie algebra. We show that the coupling of gravity to a massless scalar field leads to yet another set of constraints with the same property, albeit not as simple as that based on the coupling to dust.