Conformal Field Theories, Graphs and Quantum Algebras

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dc.creatorPetkova, Valentina
dc.creatorZuber, Jean-Bernard
dc.date2001-08-31
dc.date2001-11-14
dc.date.accessioned2026-07-07T04:12:18Z
dc.date.available2026-07-07T04:12:18Z
dc.descriptionThis article reviews some recent progress in our understanding of the structure of Rational Conformal Field Theories, based on ideas that originate for a large part in the work of A. Ocneanu. The consistency conditions that generalize modular invariance for a given RCFT in the presence of various types of boundary conditions --open, twisted-- are encoded in a system of integer multiplicities that form matrix representations of fusion-like algebras. These multiplicities are also the combinatorial data that enable one to construct an abstract ``quantum'' algebra, whose $6j$- and $3j$-symbols contain essential information on the Operator Product Algebra of the RCFT and are part of a cell system, subject to pentagonal identities. It looks quite plausible that the classification of a wide class of RCFT amounts to a classification of ``Weak $C^*$- Hopf algebras''.
dc.description23 pages, 12 figures, LateX. To appear in MATHPHYS ODYSSEY 2001 --Integrable Models and Beyond, ed. M. Kashiwara and T. Miwa, Progress in Math., Birkhauser. References and comments added
dc.identifierhttps://arxiv.org/abs/hep-th/0108236
dc.identifierhttp://arxiv.org/abs/hep-th/0108236
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/50860
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleConformal Field Theories, Graphs and Quantum Algebras
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