Noncommutative Riemann Surfaces by Embeddings in $${mathbb{R}^{3}}$$ |
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| Authors: | Joakim Arnlind Martin Bordemann Laurent Hofer Jens Hoppe Hidehiko Shimada |
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| Affiliation: | 1.Institut des Hautes études Scientifiques,Bures-sur-Yvette,France;2.Max Planck Institute for Gravitational Physics,Golm,Germany;3.Laboratoire de MIA, 4, rue des Frères Lumière,Université de Haute-Alsace,Mulhouse,France;4.Université du Luxembourg,Luxembourg City,Luxembourg;5.Department of Mathematics,KTH,Stockholm,Sweden |
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| Abstract: | We introduce C-Algebras of compact Riemann surfaces  as non-commutative analogues of the Poisson algebra of smooth functions on  . Representations of these algebras give rise to sequences of matrix-algebras for which matrix-commutators converge to Poisson-brackets as N → ∞. For a particular class of surfaces, interpolating between spheres and tori, we completely characterize (even for the intermediate singular surface) all finite dimensional representations of the corresponding C-algebras. |
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