Corona algebras and strongly self-absorbing $\mathrm{C}^{\ast}$-dynamics

[2503.07515] Corona algebras and strongly self-absorbing $\mathrm{C}^{\ast}$-dynamics Skip to main content Search Submit Donate Log in Mathematics > Operator Algebras arXiv:2503.07515 (math) [Submitted on 10 Mar 2025 ( v1 ), last revised 27 Aug 2026 (this version, v3)] Title: Corona algebras and strongly self-absorbing $\mathrm{C}^{\ast}$-dynamics Authors: Xiuyuan Li , Matteo Pagliero , Gábor Szabó View PDF HTML (experimental) Abstract: This article concerns the structure of $\mathrm{C}^{\ast}$-algebraic group actions induced on corona algebras from a given $\sigma$-unital $\mathrm{C}^{\ast}$-dynamical system over a locally compact group $G$. We prove that such actions satisfy the so-called dynamical folding property, which generalizes a fundamental property observed for corona algebras in works of Manuilov--Thomsen and Phillips--Weaver. We then focus on corona actions induced from $G$-$\mathrm{C}^{\ast}$-dynamics that are assumed to absorb a given strongly self-absorbing and unitarily regular $G$-action $\gamma$. It is proved that these corona actions are $\gamma$-saturated, which is a stronger property than being separably $\gamma$-stable. Conversely, if one assumes that the underlying $\mathrm{C}^{\ast}$-dynamics absorbs the trivial action on the compact operators, then $\gamma$-saturation of the corona action is equivalent to the original action being $\gamma$-absorbing. These results are a dynamical version of recent work by Farah and the third-named author. Comments: v2: minor updates; 21 pp. v3: minor changes; this is the final version, which will appear in Documenta Mathematica Subjects: Operator Algebras (math.OA) MSC classes: 46L05, 46L55 Cite as: arXiv:2503.07515 [math.OA] (or arXiv:2503.07515v3 [math.OA] for this version) https://doi.org/10.48550/arXiv.2503.07515 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Matteo Pagliero [ view email ] [v1] Mon, 10 Mar 2025 16:37:47 UTC (24 KB) [v2] Wed, 13 Aug 2025 13:55:24 UTC (24 KB) [v3] Thu, 27 Aug 2026 09:48:02 UTC (36 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.OA < prev | next > new | recent | 2025-03 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Corona algebras and strongly self-absorbing $\mathrm{C}^{\ast}$-dynamics#677363
• Spectroscopic structure of Non-Hermitian $\mathcal{PT}$-Symmetric Klein--Gordon Fields in a Magnetized Cosmic String Spacetime#1048735
• From quantum fluctuations to galaxy power spectrum multipoles#987037
• Estudios teóricos sobre el espectro de líneas de la corona solar, II#1089260
• Classical renormalization of the point charge#957690