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math.QA2000
Quantum tori, mirror symmetry and deformation theory
Yan Soibelman
We suggest to compactify the universal covering of the moduli space of complex structures by non-commutative spaces. The latter are described by certain categories of sheaves with…
math.QA2000
Deformations of algebras over operads and Deligne's conjecture
Maxim Kontsevich, Yan Soibelman
In present paper we develop the deformation theory of operads and algebras over operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to describe for…
math.QA1999
Meromorphic braided category arising in quantum affine algebras
Yan Soibelman
We construct a category of flat vector bundles on an elliptic curve. It arises in the representation theory of quantum affine algebras and carries meromorphic braided structure wit…