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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 163
A lattice model of local algebras of observables and fields with braid group statistics M. Karowski, R. Schrader
Using the 6j-symbols and the R-matrix for the quantum group Sl-q(2,C) at roots of unity we construct local algebras of observables and fields with braid group statistics on the lattice Z. These algebras are closely related to the XXZ-Heisenberg model and the RSOS models thus exhibiting the quantum group symmetry of these models. Our discussion relates the theory of integrable lattice models to the Doplicher-Haag-Roberts theory of superselection sectors. The construction of these algebras is a variant of the path space construction of Ocneanu and Sunders which replaces the usual tensor product construction of lattice models in statistical mechanics and extends previous discussions by Pasquier. Our construction is based on the theory of coloured graphs on S2 and the associated Wigner-Eckhart theorem obtained previously by the authors.
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