Year: 2026
Type: preprint
Abstract: We show that the Hao-Ng isomorphism for full crossed products fails to hold. More precisely, for a non-degenerate $C^*$-correspondence $X$ over a $C^*$-algebra $\mathcal{A}$ and a generalized gauge action $G \curvearrowright X$ by a locally compact group $G$, we isolate three structural obstructions for the canonical commutation $\mathcal{O}_X\rtimes G \cong \mathcal{O}_{X\rtimes G}$ between full crossed product and Cuntz-Pimsner $C^*$-algebra. The first concerns hyperrigidity, the second concerns WEP of the coefficient $C^*$-algebra $\mathcal{A}$ for trivial actions, and the third concerns the coincidence of full and reduced crossed products by the action of $G$ on $\mathcal{A}$.
Source: arXiv (Cornell University)
Authors: Dor-On, Adam, Thompson, Ian
Institutions: University of Copenhagen, University of Haifa
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: NSF-BSF: Semigroup Operator Algebras - Representations, Boundaries and Dynamics, Gruppoidmodelle für Diagramme von Gruppoidkorrespondenzen und ihre C*Algebren, Collaborative Research: NSF-BSF - Dynamics Through the Viewpoint of Self-Similar Algebras: Topological Markov Chains and Self-Similar Groups.
OpenAlex ID: W7204883984
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