Tangle and Brauer Diagram Algebras of Type Dn
Representation Theory
2007-05-23 v1 Group Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0704.2754,
title = {Tangle and Brauer Diagram Algebras of Type Dn},
author = {Arjeh M. Cohen and D. A. H. Gijsbers and David B. Wales},
journal= {arXiv preprint arXiv:0704.2754},
year = {2007}
}
Comments
33 pages