Integral modular categories and integrality of quantum invariants at rootsof unity of prime order

It is shown how to deduce integrality properties of quantum 3-manifold inva riants from the existence of integral subcategories of modular categories. The method is illustrated in the case of the invariants associated to class ical Lie algebras constructed in [42], showing that the invariants are alge braic integers provided the root of unity has prime order. This generalizes a result of [31], [32] and [29] in the sl(2)-case. We also discuss some de tails in the construction of invariants of 3-manifolds, such as the S-matri x in the PSUk case, and a local orientation reversal principle for the colo red Homfly polynomial.