Constructing Menger manifold C*-diagonals in classifiable C*-algebras

Xin Li

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arXiv · 2005.08228

Constructing Menger manifold C-diagonals in classifiable C-algebras

Xin Li

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Abstract

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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BibTeX RIS

Xin Li. 2020-05-17. Constructing Menger manifold C*-diagonals in classifiable C*-algebras. https://arxiv.org/abs/2005.08228

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