Abstract
We consider several pictures connected with non-abelian duality in 2d quantum field theory. A discrete version leads to 3d coloured pictures of quantum groups, using a non-abelian version of Poincaré duality. A continuous classical version (Poisson-Lie T-duality) have some simple mechanical analogs. Finally a connection between Poisson-Lie T-duality and Courant algebroids is presented, which conjecturaly gives a unified picture.
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References
P. Ševera, Duality and TFT: A suggestion based on d = 2 + 1, hep-th/9811136.
P. Ševera, Contact reductions, mechanics and duality, math.DS/9903168.
M. Kontsevich, Geometry of formulae, lecture given at Colloque scientifique du 40ème anniversaire, IHES, Oct. 8, 1998.
F. Klein, Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, Springer, Berlin, 1926.
C. Klimčík, P. Ševera, Dual Non-Abelian Duality and the Drinfeld Double, Phys.Lett. B351 (1995), 455–462, hep-th/9502122
J.L. Brylinski, Loop spaces, characteristic classes and geometric quantization. Progress in Mathematics, 107. Birkhäuser, Boston, 1993.
Zhang-Ju Liu, Alan Weinstein, Ping Xu, Manin Triples for Lie Bialgebroids, J. Differential Geom. 45 (1997), no. 3, 547–574.
Dmitry Roytenberg, Courant algebroids, derived brackets and even symplectic supermanifolds, UC Berkeley Ph.D. thesis, math.DG/9910078.
M. Alexandrov, M. Kontsevich, A. Schwarz, O. Zaboronsky, The Geometry of the Master Equation and Topological Quantum Field Theory, Int.J.Mod.Phys. A12 (1997), 1405–1430.
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Ševera, P. (2001). On Geometry of Non-Abelian Duality. In: Maeda, Y., Moriyoshi, H., Omori, H., Sternheimer, D., Tate, T., Watamura, S. (eds) Noncommutative Differential Geometry and Its Applications to Physics. Mathematical Physics Studies, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0704-7_13
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DOI: https://doi.org/10.1007/978-94-010-0704-7_13
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