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  Noncommutative Riemann Surfaces by Embeddings in R^3

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.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-BBD0-B Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-BBD2-7
Genre: Journal Article

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CMP288_403.pdf (Any fulltext), 430KB
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 Creators:
Arnlind, Joakim1, Author              
Bordemann, Martin, Author
Hofer, Laurent, Author
Hoppe, Jens, Author
Shimada, Hidehiko2, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:persistent22              
2Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              

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 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.

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 Dates: 2009
 Publication Status: Published in print
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 Identifiers: DOI: 10.1007/s00220-009-0766-8
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Title: Communications in Mathematical Physics
Source Genre: Journal
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Publ. Info: Heidelberg : Springer-Verlag Heidelberg
Pages: - Volume / Issue: 288 (2) Sequence Number: - Start / End Page: 403 - 429 Identifier: Other: 954925392313
Other: 0010-3616