Split extensions and KK-equivalences for quantum projective spaces

Francesca Arici; Sophie Emma Zegers

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arXiv · 2108.11360

Split extensions and KK-equivalences for quantum projective spaces

Francesca Arici·Sophie Emma Zegers

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Abstract

We study the noncommutative topology of the $C^*$-algebras $C(\mathbb{C}P_q^{n})$ of the quantum projective spaces within the framework of Kasparov's bivariant K-theory. In particular, we construct an explicit KK-equivalence with the commutative algebra $\mathbb{C}^{n+1}$. Our construction relies on showing that the extension of $C^*$-algebras relating two quantum projective spaces of successive dimensions admits a splitting, which we can describe explicitly using graph algebra techniques.

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Francesca Arici, Sophie Emma Zegers. 2021-08-25. Split extensions and KK-equivalences for quantum projective spaces. https://arxiv.org/abs/2108.11360

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