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Differential and complex geometry of two-dimensional noncommutative tori

Momar Dieng·Albert Schwarz
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Abstract

We analyze in detail projective modules over two-dimensional noncommutative tori and complex structures on these modules.We concentrate our attention on properties of holomorphic vectors in these modules; the theory of these vectors generalizes the theory of theta-functions. The paper is self-contained; it can be used also as an introduction to the theory of noncommutative spaces with simplest space of this kind thoroughly analyzed as a basic example.

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Momar Dieng, Albert Schwarz. 2002-10-28. Differential and complex geometry of two-dimensional noncommutative tori. https://arxiv.org/abs/math/0203160

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