Abstract
In two-dimensional lattice spin systems in which the spins take values in a finite groupG we find a non-Abelian “parafermion” field of the formorder x disorder that carries an action of the Hopf algebra
, the double ofG. This field leads to a “quantization” of the Cuntz algebra and allows one to define amplifying homomorphisms on the
subalgebra that create the
and generalize the endomorphisms in the Doplicher-Haag-Roberts program. The so-obtained category of representations of the observable algebra is shown to be equivalent to the representation category of
. The representation of the braid group generated by the statistics operator and the corresponding statistics parameter are calculated in each sector.
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Communicated by N. Yu. Reshetikhin
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Szlachányi, K., Vecsernyés, P. Quantum symmetry and braid group statistics inG-spin models. Commun.Math. Phys. 156, 127–168 (1993). https://doi.org/10.1007/BF02096735
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DOI: https://doi.org/10.1007/BF02096735