94 citations · 214 across the 6 of their papers we have counts for
6 papers
Representation Theory of Twisted Group Double
D. Altschuler, A. Coste, J-M. Maillard
This text collects useful results concerning the quasi-Hopf algebra $\D $. We give a review of issues related to its use in conformal theories and physical mathematics. Existence o…
Vassiliev knot invariants and Chern-Simons perturbation theory to all orders
Daniel Altschuler, Laurent Freidel
At any order, the perturbative expansion of the expectation values of Wilson lines in Chern-Simons theory gives certain integral expressions. We show that they all lead to knot inv…
Representations of knot groups and Vassiliev invariants
Daniel Altschuler
We show that the number of homomorphisms from a knot group to a finite group cannot be a Vassiliev invariant, unless it is constant on the set of torus knots. In sev…
On Universal Vassiliev Invariants
Daniel Altschuler, Laurent Freidel
Using properties of ordered exponentials and the definition of the Drinfeld associator as a monodromy operator for the Knizhnik-Zamolodchikov equations, we prove that the analytic…
Quantum Loop Modules and Quantum Spin Chains
D. Altschuler, B. Davies
We construct level-0 modules of the quantum affine algebra $\Uq$, as the -deformed version of the Lie algebra loop module construction. We give necessary and sufficient conditio…
Quasi-Quantum Groups, Knots, Three-Manifolds, and Topological Field Theory
Daniel Altschuler, Antoine Coste
We show how to construct, starting from a quasi-Hopf algebra, or quasi-quantum group, invariants of knots and links. In some cases, these invariants give rise to invariants of the…