Mathematische Annalen

, Volume 321, Issue 2, pp 347–373 | Cite as

Skein construction of idempotents in Birman-Murakami-Wenzl algebras

  • Anna Beliakova
  • Christian Blanchet


We give skein theoretic formulas for minimal idempotents in the Birman-Murakami-Wenzl algebras. These formulas are then applied to derive various known results needed in the construction of quantum invariants and modular categories. In particular, an elementary proof of the Wenzl formula for quantum dimensions is given. This proof does not use the representation theory of quantum groups and the character formulas.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Anna Beliakova
    • 1
  • Christian Blanchet
    • 2
  1. 1.Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland (e-mail:
  2. 2.LMAM, Université de Bretagne Sud, Centre Yves Coppens, BP 573, 56017 Vannes, France (e-mail:

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