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Journal Article

Noncommutative Riemann Surfaces by Embeddings in R^3

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons4309

Arnlind,  Joakim
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons20716

Shimada,  Hidehiko
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

CMP288_403.pdf
(Any fulltext), 430KB

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Citation

Arnlind, J., Bordemann, M., Hofer, L., Hoppe, J., & Shimada, H. (2009). Noncommutative Riemann Surfaces by Embeddings in R^3. Communications in Mathematical Physics, 288(2), 403-429. doi:10.1007/s00220-009-0766-8.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-BBD0-B
Abstract
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 → ∞. 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.