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Fusion structures from quantum groups: II. Why truncation is necessary

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Abstract

It is shown that a finite, reflection positive, and nontruncated fusion structure on an arbitrary Hopf algebraℋ is trivial in the sense thatq-traces coincide with ordinary traces andq-dimensions coincide with ordinary dimensions. Thus, nontruncated fusion structures are ruled out to describe the fusion rules of quantum field theories with noninteger statistical dimensions and a finite number of superselection sectors.

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Authors and Affiliations

  1. Institut für Theoretische Physik, FU-Berlin, Arnimallee 14, D-14195, Berlin, Germany

    Florian Nill

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  1. Florian Nill
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Work supported in part by DFG, SFB 288 ‘Differentialgeometrie und Quantenphysik’.

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Nill, F. Fusion structures from quantum groups: II. Why truncation is necessary. Lett Math Phys 29, 83–90 (1993). https://doi.org/10.1007/BF00749724

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  • DOI: https://doi.org/10.1007/BF00749724

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