Inductive limits of partial crossed products
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912742964723712 |
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| author | Hossain, Md Amir |
| author_facet | Hossain, Md Amir |
| contents | Let $\big((A^{(i)}, G, α^{(i)}), ϕ_i\big)_{i \in \mathbb{N}}$ be an inductive sequence of partial dynamical systems. We prove the existence of an induced partial action $α$ of $G$ on the inductive limit $A=\varinjlim A^{(i)}$. We call $α$ the inductive limit partial action. Furthermore, we show the corresponding partial crossed product $A\rtimes_αG$ is canonically isomorphic to $\varinjlim A^{(i)}\rtimes_{α^{(i)}}G$. We also study the globalization of the inductive limit partial action $α$, its finite Rokhlin dimension and tracial states on $A\rtimes_αG$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02525 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inductive limits of partial crossed products Hossain, Md Amir Operator Algebras 46L55, 18A30 Let $\big((A^{(i)}, G, α^{(i)}), ϕ_i\big)_{i \in \mathbb{N}}$ be an inductive sequence of partial dynamical systems. We prove the existence of an induced partial action $α$ of $G$ on the inductive limit $A=\varinjlim A^{(i)}$. We call $α$ the inductive limit partial action. Furthermore, we show the corresponding partial crossed product $A\rtimes_αG$ is canonically isomorphic to $\varinjlim A^{(i)}\rtimes_{α^{(i)}}G$. We also study the globalization of the inductive limit partial action $α$, its finite Rokhlin dimension and tracial states on $A\rtimes_αG$. |
| title | Inductive limits of partial crossed products |
| topic | Operator Algebras 46L55, 18A30 |
| url | https://arxiv.org/abs/2512.02525 |