On complex and noncommutative tori
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- by Igor Nikolaev PDF
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Abstract:
The ânoncommutative geometryâ of complex algebraic curves is studied. As a first step, we clarify a morphism between elliptic curves, or complex tori, and $C^*$-algebras $T_{\theta }=\{u,v~|~vu=e^{2\pi i\theta }uv\}$, or noncommutative tori. The main result says that under the morphism, isomorphic elliptic curves map to the Morita equivalent noncommutative tori. Our approach is based on the rigidity of the length spectra of Riemann surfaces.References
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Additional Information
- Igor Nikolaev
- Affiliation: Department of Mathematics, University of Calgary, 2500 University Drive N.W., Calgary, Canada T2N 1N4
- Email: nikolaev@math.ucalgary.ca
- Received by editor(s): February 25, 2003
- Received by editor(s) in revised form: November 2, 2004
- Published electronically: September 28, 2005
- Communicated by: Michael Stillman
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 973-981
- MSC (2000): Primary 14H52, 46L85
- DOI: https://doi.org/10.1090/S0002-9939-05-08244-4
- MathSciNet review: 2196027