2007/11/16 by Joakim Arnlind, Arnlind, Joakim, Martin Bordemann +7
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.0711.2588
23 pages
arxiv created 2007/11/16 · openalex publication_date 2007/11/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, nicely interpolating between spheres and tori, we completely characterize (even for the intermediate singular surface) all finite dimensional representations of the corresponding C-algebras.