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arXiv · 2604.04597

On split exact sequences and KK-equivalences of amplified graph C*-algebras

Jesse Reimann·Sophie Emma Zegers
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Abstract

We give a general methodology for constructing split exact sequences of amplified graph C*-algebras with sinks. This in turn allows us to construct explicit KK-equivalences with $\mathbb{C}^N$ for a large class of C*-algebras, including the quantum Grassmannian $\mathrm{Gr}_q(2,4)$. We discuss compatibility with known (quantum) CW-constructions and give an explicit KK-equivalence between the classical and quantum projective spaces $\mathbb{C}P^1$ and $\mathbb{C}P_q^1$.

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Jesse Reimann, Sophie Emma Zegers. 2026-04-06. On split exact sequences and KK-equivalences of amplified graph C*-algebras. https://arxiv.org/abs/2604.04597

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