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Noncommutative Riemann Surfaces by Embeddings in R3
Institut des Hautes Études Scientifiques, Le Bois-Marie 35, route de Chartres, F-91440, Bures-sur-Yvette, France och Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, D-14476, Golm, Germany .ORCID iD: 0000-0002-8727-2169
Laboratoire de MIA, 4, rue des Frères Lumière, Université de Haute-Alsace, F-68093, Mulhouse, France .
Université du Luxembourg, FSTC 162a, avenue de la Faïencerie, L-1511, Luxembourg City, Luxembourg .
Department of Mathematics, KTH, S-10044, Stockholm, Sweden .
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2009 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 288, 403-429 p.Article in journal (Refereed) Published
Abstract [en]

We introduce C-Algebras of compact Riemann surfaces Σ  as non-commutative analogues of the Poisson algebra of smooth functions on Σ  . 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

Place, publisher, year, edition, pages
Springer, 2009. Vol. 288, 403-429 p.
National Category
Mathematics Algebra and Logic
URN: urn:nbn:se:liu:diva-122356DOI: 10.1007/s00220-009-0766-8OAI: diva2:865811
Available from: 2015-10-29 Created: 2015-10-29 Last updated: 2015-11-09

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Arnlind, Joakim
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