Universal representations of braid and braid-permutation groups

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 $\mathbb{Q}$ by simple explicit formulae. We show that they give universal Vassiliev-type invariants for braid-permutation groups.

19 pages, references added

Cited by in corpus (1)

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