论文标题
由AF C* - 代理产生的痕迹
Cones of traces arising from AF C*-algebras
论文作者
论文摘要
我们表征了拓扑非现成的锥体，这些锥体可作为$ [0，\ infty] $的有限幂的投影限制。这些也是AF C*-Algebras上半连续扩展痕迹的较低的延伸痕迹的锥。我们的主要结果可能被视为任何Choquet单纯形都是有限维基质的投影限制的事实的概括。为了获得我们的主要结果，我们首先建立了具有实际乘法的某些非现实拓扑锥和Cuntz半群之间的双重性。这种双重性将紧凑型凸组和完整订单单元向量空间之间的二元性扩展到非现有设置。
We characterize the topological non-cancellative cones that are expressible as projective limits of finite powers of $[0,\infty]$. These are also the cones of lower semicontinuous extended-valued traces on AF C*-algebras. Our main result may be regarded as a generalization of the fact that any Choquet simplex is a projective limit of finite dimensional simplices. To obtain our main result, we first establish a duality between certain non-cancellative topological cones and Cuntz semigroups with real multiplication. This duality extends the duality between compact convex sets and complete order unit vector spaces to a non-cancellative setting.
