Mathematische Annalen

, Volume 321, Issue 2, pp 347–373

Skein construction of idempotents in Birman-Murakami-Wenzl algebras

  • Anna Beliakova
  • Christian Blanchet

DOI: 10.1007/s002080100233

Cite this article as:
Beliakova, A. & Blanchet, C. Math Ann (2001) 321: 347. doi:10.1007/s002080100233


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: