Stabilization theorem and symmetric structure of Cuntz--Pimsner algebras
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917516416122880 |
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| author | Mukohara, Miho Suzuki, Yuhei |
| author_facet | Mukohara, Miho Suzuki, Yuhei |
| contents | We establish a crossed product decomposition theorem for stabilized Cuntz--Pimsner algebras. This result extends Cuntz's classical decomposition for the Cuntz algebras $\mathcal{O}_n$ and reveals an implicit symmetric structure within Cuntz--Pimsner algebras. By exploiting this structure, we characterize the simplicity of these algebras and classify ideals, tracial weights, and KMS weights for generalized quasi-free flows. Our findings recover and refine seminal results in the literature, including those by Kitamura, Schweizer, and Laca--Neshveyev.
By combining our main results with the Hao--Ng isomorphism, we study quasi-free actions on $\mathcal{O}_n$. We confirm a recent question on isometrically shift-absorption posed by Izumi on compact groups. We also identify a new dichotomy for the group $G:=\mathbb{R} \times {\rm SU}(2)$: in contrast to flows, the crossed product of a quasi-free action of $G$ on $\mathcal{O}_n$ is either non-simple or purely infinite simple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21128 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stabilization theorem and symmetric structure of Cuntz--Pimsner algebras Mukohara, Miho Suzuki, Yuhei Operator Algebras We establish a crossed product decomposition theorem for stabilized Cuntz--Pimsner algebras. This result extends Cuntz's classical decomposition for the Cuntz algebras $\mathcal{O}_n$ and reveals an implicit symmetric structure within Cuntz--Pimsner algebras. By exploiting this structure, we characterize the simplicity of these algebras and classify ideals, tracial weights, and KMS weights for generalized quasi-free flows. Our findings recover and refine seminal results in the literature, including those by Kitamura, Schweizer, and Laca--Neshveyev. By combining our main results with the Hao--Ng isomorphism, we study quasi-free actions on $\mathcal{O}_n$. We confirm a recent question on isometrically shift-absorption posed by Izumi on compact groups. We also identify a new dichotomy for the group $G:=\mathbb{R} \times {\rm SU}(2)$: in contrast to flows, the crossed product of a quasi-free action of $G$ on $\mathcal{O}_n$ is either non-simple or purely infinite simple. |
| title | Stabilization theorem and symmetric structure of Cuntz--Pimsner algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2605.21128 |