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arXiv · 2303.05897

On unital absorbing extensions of C$^*$-algebras of stable rank one and real rank zero

Qingnan An·Zhicaho Liu
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Abstract

Suppose that $A,B$ are nuclear, separable ${\rm C}^*$-algebras of stable rank one and real rank zero, $A$ is unital simple, $B$ is stable and $({\rm K}_0(B),{\rm K}_0^+(B))$ is weakly unperforated in the sense of Elliott \cite{Ell}. We show that any unital extension with trivial index maps of $A$ by $B$ is absorbing.

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Qingnan An, Zhicaho Liu. 2023-03-10. On unital absorbing extensions of C$^*$-algebras of stable rank one and real rank zero. https://arxiv.org/abs/2303.05897

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