Tangle and Brauer Diagram
نویسنده
چکیده
A generalization of the Kauffman tangle algebra is given for Coxeter type Dn. The tangles involve a pole of 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 An−1. The proof involves a diagrammatic version of the Brauer algebra of type Dn of which the generalized Temperley-Lieb algebra of type Dn is a subalgebra. keywords: associative algebra, BMW algebra, Brauer algebra, TemperleyLieb algebra, tangle, Brauer diagram, Coxeter groups AMS 2000 Mathematics Subject Classification: 16K20, 17Bxx, 20F05, 20F36, 20M05, 57Mxx
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