Abstract
We show that every topological quantum field theory (understood as a functor) has an associated quasi-quantum group of internal symmetries.
Similar content being viewed by others
References
Alekseev, A. and Shatashvili, S., Quantum groups and WZW models, Chicago preprint, EFI-89-67, 1989.
Alvarez-GauméL., GomezC., and SierraG., Duality and quantum groups, Nuclear Phys. B 330, 347 (1990).
Atiyah, M. F., Hitchin, N., Lawrence, R., and Segal, G., Oxford seminar on Jones-Witten theory, Technical report, Oxford, 1988.
BouwknegtP., McCarthyJ., and PilchK., Quantum group structure in the Fock space resolutions of ŝl(n) representations, Comm. Math. Phys. 131, 125 (1990).
Drinfeld, V. G., Quasi-Hopf algebras and Knizhnik-Zamolodchikov equations, Acad. Sci. Ukr. preprint, ITP-89-43E, 1989.
FreydP. and YetterD., Braided compact closed categories with applications to low dimensional topology, Adv. Math. 77, 156–182 (1989).
Gómez, C. and Sierra, G., The quantum symmetry of rational conformal field theories, Preprint, 1990.
Joyal, A. and Street, R., Braided monoidal categories, Mathematics Reports 86008, Macquarie University, 1986.
KirillovA. A., Elements of the Theory of Representations, Springer-Verlag, Heidelberg, 1976.
Majid, S., Tannaka-Krein theorem for quasi Hopf algebras and other results (to appear in Contemp. Math.).
Majid, S., Reconstruction theorems and rational conformal field theories (to appear in Int. J. Mod. Phys. A.).
MajidS., Quasitriangular Hopf algebras and Yang-Baxter equations, Int. J. Modern Physics A 5(1), 1–91 (1990).
Ramirez, C., Ruegg, H., and Ruiz-Altaba, M., Explicit quantum symmetries of WZNW theories, Geneva preprint, UGVA-DPT 1990/06-675.
ReshetikhinN. Yu and TuraevV. G., Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127(1), 1–26 (1990).
Segal, G., The definition of conformal field theory, Technical report, Oxford, 1988.
UlbrichK.-H., On Hopf algebras and rigid monoidal categories, Israel J. Math 72, 252 (1990).
Witten, E., Some geometric applications of quantum field theory, in Proc. ICMP, Swansea, 1988. Adam Hilger.
WittenE., Topological quantum field theory, Comm. Math. Phys. 117, 353 (1988).