## Abstract

It is shown how to deduce integrality properties of quantum 3-manifold invariants from the existence of integral subcategories of modular categories. The method is illustrated in the case of the invariants associated to classical Lie algebras constructed in [42], showing that the invariants are algebraic 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 details in the construction of invariants of 3-manifolds, such as the *S*-matrix in the PSU* _{k}* case, and a local orientation reversal principle for the colored Homfly polynomial.

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