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Categories of holomorphic vector bundles on noncommutative two-tori
Alexander Polishchuk, Albert Schwarz
In this paper we study the category of standard holomorphic vector bundles on a noncommutative two-torus. We construct a functor from the derived category of such bundles to the de…
Theta-functions on noncommutative tori
Albert Schwarz
Ordinary theta-functions can be considered as holomorphic sections of line bundles over tori. We show that one can define generalized theta-functions as holomorphic elements of pro…
Projective modules over non-commutative tori: classification of modules with constant curvature connection
Alexander Astashkevich, Albert Schwarz
We study finitely generated projective modules over noncommutative tori. We prove that for every module with constant curvature connection the corresponding element of th…
Morita equivalence of multidimensional noncommutative tori
Marc Rieffel, Albert Schwarz
One can describe an -dimensional noncommutative torus by means of an antisymmetric -matrix . We construct an action of the group on the space of an…