2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78402We 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 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 topological numbers.Latex. Misprints correctedQuantum AlgebraHigh Energy Physics - Theorytext