Quantum symmetry and braid group statistics inG-spin models |
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Authors: | K Szlachányi P Vecsernyés |
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Institution: | (1) Central Research Institute for Physics, P.O. Box 49, H-1525 Budapest 114, Hungary |
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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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