Categories of holomorphic line bundles on higher dimensional noncommutative complex tori

Journal Article · Tue May 15 00:00:00 EDT 2007 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2719564· OSTI ID:20929725

Kajiura, Hiroshige ^[1]

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1. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)

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.

• OSTI ID: 20929725
• Journal Information: Journal of Mathematical Physics, Vol. 48, Issue 5; Other Information: DOI: 10.1063/1.2719564; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

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