  We introduce and study a new discrete basis of gravity constraints by making
use of harmonic expansion for closed cosmological models. The full set of
constraints is splitted into area-preserving spatial diffeomorphisms, forming
closed subalgebra, and Virasoro-like generators. Operatorial Hamiltonian
BFV-BRST quantization is performed in the framework of perturbative expansion
in the dimensionless parameter which is a positive power of the ratio of
Planckian volume to the volume of the Universe. For the (N+1) - dimensional
generalization of stationary closed Bianchi-I cosmology the nilpotency
condition for the BRST operator is examined in the first quantum approximation.
It turns out, that certain relationship between dimensionality of the space and
the spectrum of matter fields emerges from the requirement of quantum
consistency of the model.
