Noncommutative Riemann Surfaces

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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 $N\to\infty$. For a particular class of surfaces, nicely interpolating between spheres and tori, we completely characterize (even for the intermediate singular surface) all finite dimensional representations of the corresponding C-algebras.
23 pages

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Mathematical Physics, High Energy Physics - Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/142292

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0711.2588
 http://arxiv.org/abs/0711.2588

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arXiv