Abstract:
The quantum symmetry of a rational quantum field theory is a finite-dimensional multi-matrix algebra. Its representation category, which determines the fusion rules and braid group representations of superselection sectors, is a braided monoidal $C^*$-category. Various properties of such algebraic structures are described, and some ideas concerning the classification programme are outlined.
\Bibitem{Fuc94}
\by J.~Fuchs
\paper The quantum symmetry of rational field theories
\jour TMF
\yr 1994
\vol 98
\issue 3
\pages 388--403
\mathnet{http://mi.mathnet.ru/tmf1549}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1304737}
\zmath{https://zbmath.org/?q=an:0833.46058}
\transl
\jour Theoret. and Math. Phys.
\yr 1994
\vol 98
\issue 3
\pages 266--276
\crossref{https://doi.org/10.1007/BF01102203}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994PQ98700007}
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This publication is cited in the following 5 articles:
J. Mund, K.-H. Rehren, Encyclopedia of Mathematical Physics, 2006, 172
Jürgen Fuchs, Ingo Runkel, Christoph Schweigert, “TFT construction of RCFT correlators I: partition functions”, Nuclear Physics B, 646:3 (2002), 353
FRANK HAUSSER, FLORIAN NILL, “DIAGONAL CROSSED PRODUCTS BY DUALS OF QUASI-QUANTUM GROUPS”, Rev. Math. Phys., 11:05 (1999), 553
V. P. Maslov, O. Yu. Shvedov, “Complex germ method in the Fock space. II. Asymptotics, corresponding to finite-dimensional isotropic manifolds”, Theoret. and Math. Phys., 104:3 (1995), 1141–1161
V. P. Maslov, “Semiclassical asymptotics of the eigenfunctions of the Schrödinger-Hartree equation. New form of classical self-consistent field”, Theoret. and Math. Phys., 99:1 (1994), 484–493
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