Rigidity of Furstenberg entropy under ucp maps
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866910859629953024 |
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| author | Zhou, Shuoxing |
| author_facet | Zhou, Shuoxing |
| contents | Given a tracial von Neumann algebra $(M,τ)$, we prove that a state preserving $M$-bimodular ucp map between two stationary W$^*$-extensions of $(M,τ)$ preserves the Furstenberg entropy if and only if it induces an isomorphism between the Radon-Nikodym factors. With a similar proof, we extend this result to quasi-factor maps between stationary spaces of locally compact groups and prove an entropy separation between unique stationary and amenable spaces. As applications, we use these results to establish rigidity phenomena for unique stationary Poisson boundaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03424 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of Furstenberg entropy under ucp maps Zhou, Shuoxing Operator Algebras Dynamical Systems Group Theory Given a tracial von Neumann algebra $(M,τ)$, we prove that a state preserving $M$-bimodular ucp map between two stationary W$^*$-extensions of $(M,τ)$ preserves the Furstenberg entropy if and only if it induces an isomorphism between the Radon-Nikodym factors. With a similar proof, we extend this result to quasi-factor maps between stationary spaces of locally compact groups and prove an entropy separation between unique stationary and amenable spaces. As applications, we use these results to establish rigidity phenomena for unique stationary Poisson boundaries. |
| title | Rigidity of Furstenberg entropy under ucp maps |
| topic | Operator Algebras Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2503.03424 |