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http://dx.doi.org/10.4134/JKMS.2006.43.5.951

A TOPOLOGICAL MIRROR SYMMETRY ON NONCOMMUTATIVE COMPLEX TWO-TORI  

Kim, Eun-Sang (Department of Applied Mathematics Hanyang University)
Kim, Ho-Il (Department of Mathematics Kyungpook National University)
Publication Information
Journal of the Korean Mathematical Society / v.43, no.5, 2006 , pp. 951-965 More about this Journal
Abstract
In this paper, we study a topological mirror symmetry on noncommutative complex tori. We show that deformation quantization of an elliptic curve is mirror symmetric to an irrational rotation algebra. From this, we conclude that a mirror reflection of a noncommutative complex torus is an elliptic curve equipped with a Kronecker foliation.
Keywords
noncommutative complex torus; mirror symmetry; Kronecker foliation;
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