The quantum symmetry of rational field theories
Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 3, pp. 388-403 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
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J. Fuchs. The quantum symmetry of rational field theories. Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 3, pp. 388-403. http://geodesic.mathdoc.fr/item/TMF_1994_98_3_a8/

[1] S. Doplicher, R. Haag, J. E. Roberts, Commun. Math. Phys., 13 (1969), 1 | DOI | MR | Zbl

[2] S. Doplicher, R. Haag, J. E. Roberts, Commun. Math. Phys., 35 (1974), 49 | DOI | MR

[3] D. Kastler, M. Mebkhout, K.-H. Rehren, The Algebraic Theory of Sniper selection Sectors. Introduction and Recent Results, ed. D. Kastler, World Scientific, Singapore, 1990, 356 | MR

[4] R. Haag, Local Quantum Physics, Springer-Verlag, Berlin, 1992 | MR | Zbl

[5] V. S. Sunder, An Invitation to von Neumann Algebras, Springer-Verlag, New York, 1986 | MR | Zbl

[6] F. Murray, J. von Neumann, Ann. Math., 44 (1943), 716 | DOI | MR | Zbl

[7] V. F. R. Jones, Invent. math., 72 (1983), 1 | DOI | MR | Zbl

[8] F. M. Goodman, P. de la Harpe, V. F. R. Jones, Coxeter Graphs and Towers of Algebras, MSRI Publications, 14, Springer-Verlag, New York, 1989 | MR | Zbl

[9] K.-H. Rehren, The Algebraic Theory of Superselection Sectors. Introduction and Recent Results, ed. D. Kastler, World Scientific, Singapore, 1990, 333 | MR

[10] J. Fuchs, Proceedings of the XXV. International Symposium Ahrenshoop on the Theory of Elementary Particles, ed. H. J. Kaiser, DESY publication, Hamburg/Zeuthen, 1992, 99

[11] K. Fredenhagen, K.-H. Rehren, B. Schroer, Rev. Math. Phys., 1992, 113–157, Special Issue | DOI | MR | Zbl

[12] F. Gabbiani, J. Fröhlich, Commun. Math. Phys., 155 (1993), 569 | DOI | MR | Zbl

[13] R. Brunetti, D. Guido, R. Longo, Commun. Math. Phys., 156 (1993), 201 | DOI | MR | Zbl

[14] P. Vecsernyés, On the quantum symmetry of the chiral Ising model, preprint PUPT-1406, Princeton, 1993 | MR | Zbl

[15] K. Szlachányi, Chiral decomposition as a source of quantum symmetry in the Ising model, preprint, Budapest, 1993 | MR

[16] K.-H. Rehren, Mathematical Physics X, ed. K. Schmüdgen, Springer-Verlag, Berlin, 1992, 388 | MR | Zbl

[17] J. Fröhlich, T. Kerler, Quantum Groups, Quantum Categories and Quantum Field Theory, Springer Lecture Notes in Mathematics, 1542, Springer-Verlag, Berlin, 1993 | DOI | MR | Zbl

[18] J. Fuchs, P. van Driel, Lett. Math. Phys., 23 (1991), 11 | DOI | MR | Zbl

[19] J. Fuchs, Int. J. Mod. Phys. B, 6 (1992), 1951 | DOI | MR | Zbl

[20] F. Nill, Fusion structures from quantum groups. II. Why truncation is necessary, preprint, Berlin, 1993 | MR | Zbl

[21] H. Kratz, Phys. Lett. B, 317 (1993), 60 | DOI | MR

[22] R. Häring, Quantum symmetry, preprint, Frankfurt, 1993

[23] K. Szlachányi, P. Vecsernyés, in preparation

[24] G. Mack, V. Schomerus, Nucl. Phys. B, 370 (1992), 185 | DOI | MR

[25] J. Fuchs, preprint CERN-TH.6513/92

[26] V. G. Drinfeld, Leningrad Math. J., 1 (1990), 1419 | MR | Zbl

[27] G. Moore, N. Seiberg, Commun. Math. Phys., 123 (1989), 177 | DOI | MR | Zbl

[28] L. Alvarez-Gaumé, C. Gómez, G. Sierra, The Physics and Mathematics of Strings (Memorial Volume), eds. V. G. Knizhnik, L. Brink et al., World Scientific, Singapore, 1990, 16 | DOI | MR

[29] S. Doplicher, J. E. Roberts, Bull. Amer. Math. Soc., 11 (1984), 333 | DOI | MR | Zbl

[30] S. Doplicher, J. E. Roberts, Invent. math., 98 (1989), 157 | DOI | MR | Zbl

[31] P. Furlan, A. Ch. Ganchev, V. B. Petkova, Nucl. Phys. B, 343 (1990), 205 | DOI | MR

[32] G. Mack, V. Schomerus, Phys. Lett. B, 267 (1991), 207 | DOI | MR

[33] J. Fuchs, Affine Lie Algebras and Quantum Groups, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1992 | MR | Zbl

[34] V. Chari, A. N. Pressley, A Guide to Quantum Groups, Cambridge University Press, Cambridge, 1993 | MR

[35] J. Fuchs, A. Ch. Ganchev, P. Vecsernyés, in preparation