2007/04/20 by Arjeh M. Cohen, Cohen, Arjeh M., D. A. H. Gijsbers +3
Mathematics · #16K20 #17Bxx #20F05 #20F36 #20M05 #57Mxx #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:16K20 #msc:17Bxx #msc:20F05 #msc:20F36 #msc:20M05 #msc:57Mxx
paper · pdf · doi:10.48550/arxiv.0704.2754
33 pages
arxiv created 2007/04/20 · arxiv updated 2009/12/01
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.