On complex and noncommutative tori
代数几何
2009-01-26 v2 算子代数
摘要
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.
引用
@article{arxiv.math/0212324,
title = {On complex and noncommutative tori},
author = {Igor Nikolaev},
journal= {arXiv preprint arXiv:math/0212324},
year = {2009}
}
备注
13 pages, straighten version, to appear Proc. Amer. Math. Soc