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

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

1999-04-25

arxiv.org/abs/math/9904139v2

Mathematics

Quantum Algebra

Latex. Misprints corrected

Scientific paper

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 such a module $E$ with constant curvature connection that $[E] = \mu $. In physical words we give necessary and sufficient conditions for existence of 1/2 BPS states in terms of topological numbers.

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