Communications in Mathematical Physics

, Volume 156, Issue 1, pp 127–168 | Cite as

Quantum symmetry and braid group statistics inG-spin models

  • K. Szlachányi
  • P. Vecsernyés


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.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • K. Szlachányi
    • 1
  • P. Vecsernyés
    • 1
  1. 1.Central Research Institute for PhysicsBudapest 114Hungary

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