Classification of Holomorphic Vector Bundles on Noncommutative Two-Tori

We prove that every holomorphic vector bundle on a noncommutative two-torus $T$ can be obtained by successive extensions from standard holomorphic bundles considered in [2]. This implies that the category of holomorphic bundles on $T$ is equivalent to the heart of a certain $t$-structure on the derived category of coherent sheaves on an elliptic curve.

2000 Mathematics Subject Classification:

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