Algebraic quantization of the closed bosonic string

The gauge invariant observables of the closed bosonic string are quantized in four space-time dimensions by constructing their quantum algebra in a manifestly covariant approach, respecting all symmetries of the classical observables. The quantum algebra is the kernel of a derivation on the universal enveloping algebra of an infinite-dimensional Lie algebra. The search for Hubert space representations of this algebra is separated from its construction, and postponed.