A pr 1 99 9 Projective modules over non-commutative tori : classification of modules with constant curvature connection

@inproceedings{Astashkevich2008AP1,
  title={A pr 1 99 9 Projective modules over non-commutative tori : classification of modules with constant curvature connection},
  author={Alexander Astashkevich and Albert Schwarz},
  year={2008}
}
We study finitely generated projective modules over noncommutative tori. We prove that for every module E with a 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 such a module E with constant curvature connection that [E] = μ. In physical words we give necessary and sufficient conditions for existence of 1/2 BPS states in terms of… CONTINUE READING