Tangle and Brauer Diagram Algebras of Type Dn

Details Tangle and Brauer Diagram Algebras of Type Dn Tangle and Brauer Diagram Algebras of Type Dn

2007-04-20

arxiv.org/abs/0704.2754v1

Mathematics

Representation Theory

33 pages

Scientific paper

A generalization of the Kauffman tangle algebra is given for Coxeter type Dn. The tangles involve a pole or order 2. The algebra is shown to be isomorphic to the Birman-Murakami-Wenzl algebra of the same type. This result extends the isomorphism between the two algebras in the classical case, which in our set-up, occurs when the Coxeter type is of type A with index n-1. The proof involves a diagrammatic version of the Brauer algebra of type Dn in which the Temperley-Lieb algebra of type Dn is a subalgebra.

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