Morphisms of Cuntz-Pimsner algebras from completely positive maps
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929408649986048 |
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| author | Brix, Kevin Aguyar Mundey, Alexander Rennie, Adam |
| author_facet | Brix, Kevin Aguyar Mundey, Alexander Rennie, Adam |
| contents | We introduce positive correspondences as right C*-modules with left actions given by completely positive maps. Positive correspondences form a semi-category that contains the C*-correspondence (Enchilada) category as a "retract". Kasparov's KSGNS construction provides a semi-functor from this semi-category onto the C*-correspondence category. The need for left actions by completely positive maps appears naturally when we consider morphisms between Cuntz-Pimsner algebras, and we describe classes of examples arising from projections on C*-correspondences and Fock spaces, as well as examples from conjugation by bi-Hilbertian bimodules of finite index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16600 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Morphisms of Cuntz-Pimsner algebras from completely positive maps Brix, Kevin Aguyar Mundey, Alexander Rennie, Adam Operator Algebras 46L55 (Primary), 37A55, 46L08 (Secondary) We introduce positive correspondences as right C*-modules with left actions given by completely positive maps. Positive correspondences form a semi-category that contains the C*-correspondence (Enchilada) category as a "retract". Kasparov's KSGNS construction provides a semi-functor from this semi-category onto the C*-correspondence category. The need for left actions by completely positive maps appears naturally when we consider morphisms between Cuntz-Pimsner algebras, and we describe classes of examples arising from projections on C*-correspondences and Fock spaces, as well as examples from conjugation by bi-Hilbertian bimodules of finite index. |
| title | Morphisms of Cuntz-Pimsner algebras from completely positive maps |
| topic | Operator Algebras 46L55 (Primary), 37A55, 46L08 (Secondary) |
| url | https://arxiv.org/abs/2311.16600 |