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

Alexander Astashkevich·Albert Schwarz
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Abstract

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 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.

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Alexander Astashkevich, Albert Schwarz. 2000-04-27. Projective modules over non-commutative tori: classification of modules with constant curvature connection. https://arxiv.org/abs/math/9904139

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