2005/10/14 by Hiroshige Kajiura
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Differential (mechanical device) #Differential form #Holomorphic function #Homotopy and Cohomology in Algebraic Topology #Noncommutative algebraic geometry #Noncommutative geometry #Noncommutative quantum field theory #Quantum differential calculus #Torus #hep-th #math.AG #math.QA
paper · pdf · doi:10.1063/1.2719564
published as J.Math.Phys.48:053517,2007 · 28 pages
arxiv created 2005/10/14 · openalex publication_date 2007/05/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We construct explicitly noncommutative deformations of categories of holomorphic line bundles over higher dimensional tori. Our basic tools are Heisenberg modules over noncommutative tori and complex∕holomorphic structures on them introduced by Schwarz [“Theta functions on noncommutative tori,” Lett. Math. Phys. 58, 81–90 (2001)]. We obtain differential graded (DG) categories as full subcategories of curved DG categories of Heisenberg modules over the complex noncommutative tori. Also, we present the explicit composition formula of morphisms, which, in fact, depends on the noncommutativity.