Real rank of extensions of C*-algebras

Hannes Thiel

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arXiv · 2311.03403

Real rank of extensions of C*-algebras

Hannes Thiel

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Abstract

Given a closed ideal $I$ in a C*-algebra $A$, we develop techniques to bound the real rank of $A$ in terms of the real ranks of $I$ and $A/I$. Building on work of Brown, Lin and Zhang, we obtain complete solutions if $I$ belongs to any of the following classes: (1) C*-algebras with real rank zero, stable rank one and vanishing $K_1$-group; (2) simple, purely infinite C*-algebras; (3) simple, $\mathcal{Z}$-stable C*-algebras with real rank zero; (4) separable, stable C*-algebras with an approximate unit of projections and the Corona Factorization Property.

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BibTeX RIS

Hannes Thiel. 2023-11-05. Real rank of extensions of C*-algebras. https://arxiv.org/abs/2311.03403

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