# Skein construction of idempotents in Birman-Murakami-Wenzl algebras

Beliakova, A; Blanchet, C (2001). Skein construction of idempotents in Birman-Murakami-Wenzl algebras. Mathematische Annalen, 321(2):347-373.

## Abstract

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.

## Abstract

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.

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