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arXiv · 2401.01725

KK-duality for the Cuntz-Pimsner algebras of Temperley-Lieb subproduct systems

Francesca Arici·Dimitris Michail Gerontogiannis·Sergey Neshveyev
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Abstract

We prove that the Cuntz-Pimsner algebra of every Temperley-Lieb subproduct system is KK-self-dual. We show also that every such Cuntz-Pimsner algebra has a canonical KMS-state, which we use to construct a Fredholm module representative for the fundamental class of the duality. This allows us to describe the K-homology of the Cuntz-Pimsner algebras by explicit Fredholm modules. Both the construction of the dual class and the proof of duality rely in a crucial way on quantum symmetries of Temperley-Lieb subproduct systems. In the simplest case of Arveson's $2$-shift our work establishes $U(2)$-equivariant KK-self-duality of $S^3$.

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Francesca Arici, Dimitris Michail Gerontogiannis, Sergey Neshveyev. 2024-01-03. KK-duality for the Cuntz-Pimsner algebras of Temperley-Lieb subproduct systems. https://arxiv.org/abs/2401.01725

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