  We consider quantum invariants of 3-manifolds associated with arbitrary
simple Lie algebras. Using the symmetry principle we show how to decompose the
quantum invariant as the product of two invariants, one of them is the
invariant corresponding to the projective group. We then show that the
projective quantum invariant is always an algebraic integer, if the quantum
parameter is a prime root of unity. We also show that the projective quantum
invariant of rational homology 3-spheres has a perturbative expansion a la
Ohtsuki. The presentation of the theory of quantum 3-manifold is
self-contained.
