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Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories
September 23-28, 2002
Fields Institute
Toronto, ON, Canada

Organizers
George Janelidze, Georgian Academy of Sciences, Bodo Pareigis, University of Munich, Walter Tholen, York University

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Pure braided Hopf algebras and knot invariants
by
Mihai D. Staic
SUNY at Buffalo

Quasitriangular Hopf algebras give representations for the braid group Bn. Using representations obtained in this way there were obtained invariants for knots, links and 3-manifolds. The pure braid group is the kernel of the obvious morphism from Bn to the symetric group. We shall present a method to construct representations for Pn starting with a 2-cocycle T which satifies some extra conditions. This method is similar with the one that gives representations for Bn starting from a quasitriangular Hopf algebra. Using this representation we construct invariants for long knots. There are also some categorical formulations for this concept. It worth to mentions that there is a natural definitions for ribbon categories as an intrinsec notion (in the absence of a braiding of any kind).

Date received: May 15, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajf-09.