Quantum symmetry and braid group statistics inG-spin models

@article{Szlachnyi1993QuantumSA,
  title={Quantum symmetry and braid group statistics inG-spin models},
  author={Korn{\'e}l Szlach{\'a}nyi and P{\'e}ter Vecserny{\'e}s},
  journal={Communications in Mathematical Physics},
  year={1993},
  volume={156},
  pages={127-168}
}
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… 
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