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Universal representations of braid and braid-permutation groups

Authors
  • Berceanu, Barbu
  • Papadima, Stefan
Type
Published Article
Publication Date
Oct 24, 2009
Submission Date
Aug 04, 2007
Source
arXiv
License
Yellow
External links

Abstract

Drinfel'd used associators to construct families of universal representations of braid groups. We consider semi-associators (i.e., we drop the pentagonal axiom and impose a normalization in degree one). We show that the process may be reversed, to obtain semi-associators from universal representations of 3-braids. We view braid groups as subgroups of braid-permutation groups. We construct a family of universal representations of braid-permutation groups, without using associators. All representations in the family are faithful, defined over $\bbQ$ by simple explicit formulae. We show that they give universal Vassiliev-type invariants for braid-permutation groups.

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