On complex and noncommutative tori
Algebraic Geometry
2009-01-26 v2 Operator Algebras
Abstract
The "noncommutative geometry" of complex algebraic curves is studied. As first step, we clarify a morphism between elliptic curves, or complex tori, and C*-algebras T_t={u,v | vu=exp(2\pi it)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.
Keywords
Cite
@article{arxiv.math/0212324,
title = {On complex and noncommutative tori},
author = {Igor Nikolaev},
journal= {arXiv preprint arXiv:math/0212324},
year = {2009}
}
Comments
13 pages, straighten version, to appear Proc. Amer. Math. Soc