# 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…

## 67 Citations

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### The structure of the observable algebra determined by a Hopf *-subalgebra in Hopf spin models

- MathematicsFilomat
- 2021

Let H be a finite dimensional Hopf C*-algebra, H1 a Hopf*-subalgebra of H.
This paper focuses on the observable algebra AH1 determined by H1 in
nonequilibrium Hopf spin models, in which there is a…

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