可分类C* 代数中Menger流形C*-对角的构造
Constructing Menger manifold C*-diagonals in classifiable C*-algebras
摘要：
在所有可分类的连续标度无单位或稳定无投影的稳定有限C* 代数中，构造了具有连通谱的C*-对角.对于具有无挠$K_0$和平凡$K_1$的可分类的稳定有限C* 代数，我们进一步确定了C*-对角直到同胚的谱。在幺正的情况下，底层空间是门格尔曲线。在稳定无投影的情况下，该空间是通过从门格尔曲线中移除康托空间的非局部分离副本而获得的。我们证明了每个可分类C* 代数-代数都有连续的多个两两非共轭的Menger流形C*-对角线。同时，我们也得到了所有一维非交换CW复形中C*-对角的完全分类。
英文摘要：
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.
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