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By A. Jaffe (Chief Editor)

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Extra info for Communications in Mathematical Physics - Volume 202

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Nest (1) T2θ is simple for θ irrational; (2) T2θ is isomorphic to a twisted group C*-algebra C ∗ (Z2 , ωθ ) for an appropriate element ωθ of the second cohomology group of Z2 with values in the unit circle; (3) θ → T2θ is a strict deformation quantisation of the Poisson manifold (T2 , { , }) (where { , } is the standard Poisson structure of T2 ) in the sense of M. A. e. there exists a family of maps: θ → πθ : C ∞ (T2 ) → T2θ such that for each θ the range of πθ is dense and 1 ||πθ (f )πθ (g) − πθ (f g + 2πθ{f, g})|| −→ 0.

Math. : On flatness of Ocneanu’s connection on Dynkin diagrams and classification of subfactors. J. Funct. Anal. 127, 63–107 (1995) [O1] Ocneanu, A. Quantized group, string algebras and Galois theory for algebras. In: Operator algebras and applications, Vol. 2. London Math. Soc. Lecture Notes Series 136, 1989, pp. : Quantum symmetry, differential geometry of finite graphs and classification of subfactors. Univ. of Tokyo Seminary Note 45, recorded by Y. : Paths on Coxeter Diagrams: From Platonic solids and singularities to minimal models and subfactors.

Math. 92, 349–384 (1988) [H] Communicated by H. Araki Commun. Math. Phys. 202, 65 – 87 (1999) Communications in Mathematical Physics © Springer-Verlag 1999 Topological Approach to Quantum Surfaces Toshikazu Natsume1 , Ryszard Nest2 1 2 School of Mathematics, Nagoya Institute of Technology, Showa-ku, Nagoya 466, Japan Mathematics Institute, University of Copenhagen, Universitetsparken 5, Copenhagen, DK-2100 Ø, Denmark Received: 11 June 1998 / Accepted: 28 July 1998 Abstract: We discuss a topological method to quantize closed surfaces.

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