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math.QA2001
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…
math.QA1999
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…
math.QA1998
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…