Astashkevich, Alexander; Schwarz, Albert Projective modules over non-commutative tori: classification of modules with constant curvature connection. (English) Zbl 0996.46031 J. Oper. Theory 46, No. 3, 619-634 (2001). Summary: 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 \(\mu\) in the K-group one can find a module \(E\) with constant curvature connection such that \([E]=\mu\). In physical words we give necessary and sufficient conditions for existence of \(1/2\) BPS states in terms of topological numbers. Cited in 5 Documents MSC: 46L87 Noncommutative differential geometry 81T75 Noncommutative geometry methods in quantum field theory 58B34 Noncommutative geometry (à la Connes) 46L08 \(C^*\)-modules Keywords:non-commutative torus; constant curvature connection; K-group × Cite Format Result Cite Review PDF Full Text: arXiv