Physics – Mathematical Physics
Scientific paper
2007-11-16
Physics
Mathematical Physics
23 pages
Scientific paper
We introduce C-Algebras of compact Riemann surfaces $\Sigma$ as non-commutative analogues of the Poisson algebra of smooth functions on $\Sigma$. 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.
Arnlind Joakim
Bordemann Martin
Hofer Laurent
Hoppe Jens
Shimada Hidehiko
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