An algebra of observables for de Sitter space

We describe an algebra of observables for a static patch in de Sitter space, with operators gravitationally dressed to the worldline of an observer. The algebra is a von Neumann algebra of Type II₁. There is a natural notion of entropy for a state of such an algebra. There is a maximum entropy state, which corresponds to empty de Sitter space, and the entropy of any semiclassical state of the Type II₁ algebras agrees, up to an additive constant independent of the state, with the expected generalized entropy S_gen = (A/4G_N) + S_out. An arbitrary additive constant is present because of the renormalization that is involved in defining entropy for a Type II₁ algebra.