论文标题
在可分类的C* - 代数中构建Menger歧管C*-diagonals
Constructing Menger manifold C*-diagonals in classifiable C*-algebras
论文作者
论文摘要
我们在所有可分类的稳定c* - 代数中构建具有连接光谱的C*-DiaGonals，它们在连续尺度上是UNITAL或稳定不明的。对于可分类的稳定有限的C* - 代数，无扭转$ k_0 $和琐碎的$ k_1 $，我们进一步确定了c* - diagonals的光谱，直到同构。在Unital的情况下，底层空间被证明是Menger曲线。在稳定的投射情况下，通过从Menger曲线中去除康托尔空间的非零分离副本来获得空间。我们表明，我们每个可分类的C* - 代数都具有许多成对的非偶联的c*-diagonals。一路走来，我们还获得了所有一维非公共CW复合物中c*-diagonals的完整分类。
We construct C*-diagonals with connected spectra in all classifiable stably finite C*-algebras which are unital or stably projectionless with continuous scale. For classifiable stably finite C*-algebras with torsion-free $K_0$ and trivial $K_1$, we further determine the spectra of the C*-diagonals up to homeomorphism. In the unital case, the underlying space turns out to be the Menger curve. In the stably projectionless case, the space is obtained by removing a non-locally-separating copy of the Cantor space from the Menger curve. We show that each of our classifiable C*-algebras has continuum many pairwise non-conjugate such Menger manifold C*-diagonals. Along the way, we also obtain a complete classification of C*-diagonals in all one-dimensional non-commutative CW complexes.
