تقرير
KK-duality for the Cuntz-Pimsner algebras of Temperley-Lieb subproduct systems
| العنوان: | KK-duality for the Cuntz-Pimsner algebras of Temperley-Lieb subproduct systems |
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| المؤلفون: | Arici, Francesca, Gerontogiannis, Dimitris Michail, Neshveyev, Sergey |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Operator Algebras, Mathematics - K-Theory and Homology, Mathematics - Quantum Algebra, 46L52, 46L67, 46L85 (primary), 19K35 (secondary) |
| الوصف: | 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 $S^3$. Comment: 20 pages; v2: minor corrections |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.01725 |
| رقم الأكسشن: | edsarx.2401.01725 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |