Cuntz-Nica-Pimsner algebras of product systems over groupoids
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913190036635648 |
|---|---|
| author | Amini, Massoud Moosazadeh, Mahdi |
| author_facet | Amini, Massoud Moosazadeh, Mahdi |
| contents | Let $X$ be a product system over a quasi-lattice ordered groupoid $(G,P)$. Under mild hypotheses, we associate to $X$ a $C^*$-algebra which is couniversal for injective Nica covariant Toeplitz representations of $X$ which preserve the gauge coaction. When $(G,P)$ is a quasi-lattice ordered group this couniversal $C^*$-algebra coincides with the Cuntz-Nica-Pimsner algebra introduced by Carlsen-Larsen-Sims-Vittadello, and under some mild amenability conditions with that of Sims and Yeend. We prove related gauge invariant uniqueness theorems in this general setup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10923 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cuntz-Nica-Pimsner algebras of product systems over groupoids Amini, Massoud Moosazadeh, Mahdi Operator Algebras 46L05 Let $X$ be a product system over a quasi-lattice ordered groupoid $(G,P)$. Under mild hypotheses, we associate to $X$ a $C^*$-algebra which is couniversal for injective Nica covariant Toeplitz representations of $X$ which preserve the gauge coaction. When $(G,P)$ is a quasi-lattice ordered group this couniversal $C^*$-algebra coincides with the Cuntz-Nica-Pimsner algebra introduced by Carlsen-Larsen-Sims-Vittadello, and under some mild amenability conditions with that of Sims and Yeend. We prove related gauge invariant uniqueness theorems in this general setup. |
| title | Cuntz-Nica-Pimsner algebras of product systems over groupoids |
| topic | Operator Algebras 46L05 |
| url | https://arxiv.org/abs/2312.10923 |