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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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

G Masbaum
  • Institut de Mathematiques de Jussieu, UMR 7586 CNRS, Université Paris VII, Case 7012, 2 pl. Jussieu, F-75251 Paris Cedex 05.
  • :
/ H Wenzl
  • Department of Mathematics, UC San Diego, La Jolla CA 92093-0112, USA.
  • :
Published Online: 2008-06-11 | DOI: https://doi.org/10.1515/crll.1998.505.209


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 sl2-case. We also discuss some details in the construction of invariants of 3-manifolds, such as the S-matrix in the PSUk case, and a local orientation reversal principle for the colored Homfly polynomial.

Received: 1997-03-21

Accepted: 1998-06-24

Published Online: 2008-06-11

Published in Print: 1998-12-16

Citation 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

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