103 citations · 686 across the 101 of their papers we have counts for
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Massey products on cycles of projective lines and trigonometric solutions of the Yang-Baxter equations
Alexander Polishchuk
We show that a nondegenerate unitary solution of the associative Yang-Baxter equation (AYBE) for $\Mat(N,\C)$ (see math.AG/0008156) with the Laurent series at of the…
Quasicoherent sheaves on complex noncommutative two-tori
Alexander Polishchuk
We introduce the notion of a quasicoherent sheaf on a complex noncommutative two-torus as an ind-object in the category of holomorphic vector bundles on . Extending the resu…
Analogues of the exponential map associated with complex structures on noncommutative two-tori
Alexander Polishchuk
We define and study analogues of exponentials for functions on noncommutative two-tori that depend on a choice of a complex structure. The major difference with the commutative cas…
Classification of holomorphic vector bundles on noncommutative two-tori
Alexander Polishchuk
We prove that every holomorphic vector bundle on a noncommutative two-torus can be obtained by successive extensions from standard holomorphic bundles considered in math.QA/021…
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…