Projective modules over non-commutative tori: classification of modules with constant curvature connection

摘要

We study finitely generated projective modules over noncommutative tori. We prove that for every module E with constant curvature connection the corresponding element [E] of the K-group is a generalized quadratic exponent and, conversely, for every positive generalized quadratic exponent μ in the K-group one can find a module E with constant curvature connection such that [E] = μ. In physical words we give necessary and sufficient conditions for existence of 1/2 BPS states in terms of topological numbers.