Differential and complex geometry of two-dimensional noncommutative tori

2002/03/15 by Momar Dieng, Albert Schwarz, Dieng, Momar +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/0203160

final draft

openalex publication_date 2002/03/15 · arxiv created 2002/10/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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.

Citations

• Gauge theories on noncommutative spaces
• Real Multiplication and noncommutative geometry
• Projective Modules over Higher-Dimensional Non-Commutative Tori

Cited by

• Gauge fields on tori and T-duality
• Theta functions on noncommutative T4

Related

• Theta-functions on noncommutative tori
• Generalized theta functions, projectively flat vector bundles and noncommutative tori
• Projective module description of embedded noncommutative spaces
• Noncommutative two-tori with real multiplication as noncommutative projective varieties
• Examples of noncommutative manifolds: complex tori and spherical manifolds