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, Volume 93, Issue 1, pp 163–176 | Cite as

On tensor representations of knot algebras

  • Tammo tom Dieck


The fact that a Yang-Baxter operator defines tensor representations of the Artin braid group has been used to construct knot invariants. The main purpose of this note is to extend the tensor representations of the Artin braid group to representations of the braid groupZ B k associated to the Coxeter graphB k. This extension is based on some fundamental identities for the standardR-matrices of quantum Lie theory, here called four braid relations. As an application, tensor representations of knot algebras of typeB (Hecke, Temperley-Lieb, Birman-Wenzl-Murakami) are derived.

Subject classification

57M25 17B37 

Key words

Braid groups of Coxeter typeA andB Yang-Baxter operators tensor representations knot algebras 


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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Tammo tom Dieck
    • 1
  1. 1.Mathematisches InstitutGöttingen

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