非交换环面上的投射模：常曲率联络模的分类
Projective modules over non-commutative tori: classification of modules with constant curvature connection
摘要：
研究了非交换环面上的n-生成投射模。证明了对每个常曲率联络模$E$，K-群中相应的元$[E]$是广义二次指数，反之，对K-群中每个正的广义二次指数$μ$，都能找到这样一个常曲率联络模$E$，即$[E] = μ$ .在物理上，我们用拓扑数给出了1/2 BPS态存在的充要条件。
英文摘要：
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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