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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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$C^*$ tensor categories from quantum groups
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by Hans Wenzl
J. Amer. Math. Soc. 11 (1998), 261-282


Let $\mathfrak g$ be a semisimple Lie algebra and let $d$ be the ratio between the square of the lengths of a long and a short root. Moreover, let $\mathcal F$ be the quotient category of the category of tilting modules of $U_q\mathfrak g$ modulo the ideal of tilting modules with zero $q$-dimension for $q=e^{\pm \pi i/dl}$. We show that for $l$ a sufficiently large integer, the morphisms of $\mathcal F$ are Hilbert spaces satisfying functorial properties. As an application, we obtain a subfactor of the hyperfinite II$_1$ factor for each object of $\mathcal F$.
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Bibliographic Information
  • Hans Wenzl
  • Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112
  • MR Author ID: 239252
  • Email:
  • Received by editor(s): February 7, 1997
  • Received by editor(s) in revised form: September 29, 1997
  • Additional Notes: The author was supported in part by NSF grant # DMS 94-00987
  • © Copyright 1998 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 11 (1998), 261-282
  • MSC (1991): Primary 81R50, 46L37
  • DOI:
  • MathSciNet review: 1470857