## 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.

Received: 1997-03-21Accepted: 1998-06-24Published Online: 2008-06-11Published in Print: 1998-12-16Citation Information:Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 1998, Issue 505, Pages 209–235, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crll.1998.505.209, June 2008