KK-duality for the Cuntz-Pimsner algebras of Temperley-Lieb subproduct systems
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913234845433856 |
|---|---|
| author | Arici, Francesca Gerontogiannis, Dimitris Michail Neshveyev, Sergey |
| author_facet | Arici, Francesca Gerontogiannis, Dimitris Michail Neshveyev, Sergey |
| contents | 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 $S^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01725 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | KK-duality for the Cuntz-Pimsner algebras of Temperley-Lieb subproduct systems Arici, Francesca Gerontogiannis, Dimitris Michail Neshveyev, Sergey Operator Algebras K-Theory and Homology Quantum Algebra 46L52, 46L67, 46L85 (primary), 19K35 (secondary) 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 $S^3$. |
| title | KK-duality for the Cuntz-Pimsner algebras of Temperley-Lieb subproduct systems |
| topic | Operator Algebras K-Theory and Homology Quantum Algebra 46L52, 46L67, 46L85 (primary), 19K35 (secondary) |
| url | https://arxiv.org/abs/2401.01725 |