arXiv subjects

Matteo Pagliero

Publications and source records attributed to Matteo Pagliero.

5 recordsLinked to original sources

arXiv2026

Pureness and stable rank one for reduced twisted group $\mathrm{C}^\ast$-algebras of certain group extensions

The purpose of this note is to prove two results. First, we observe that discrete groups with property $\mathrm{P}_{\mathrm{PHP}}$ in the sense of Ozawa give rise to completely selfless reduced twisted group $\mathrm{C}^\ast$-algebras, thereby extending a theorem of Ozawa from the untwisted to the twisted case. We also observe that an adaptation of property $\mathrm{P}_{\mathrm{PHP}}$ for an inclusion of groups implies that the associated inclusion of reduced twisted group $\mathrm{C}^\ast$-algebras is selfless in the sense of Hayes-Kunnawalkam Elayavalli-Patchell-Robert. Second, we show that reduced (twisted) $\mathrm{C}^\ast$-algebras of some group extensions of the form finite-by-$G$, with $G$ having the property $\mathrm{P}_{\mathrm{PHP}}$, have stable rank one and are pure, which implies strict comparison. Our results do not assume rapid decay, and extend a theorem of Raum-Thiel-Vilalta. Examples covered by our results include reduced twisted group $\mathrm{C}^\ast$-algebras of all acylindrically hyperbolic groups and all lattices in ${\rm SL}(n,\mathbb R)$ for $n\geq2$.

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arXiv2025

Selfless reduced free products and graph products of $\mathrm{C}^\ast$-algebras

Under mild assumptions, we show that reduced free products and reduced graph products of $\mathrm{C}^{\ast}$-algebras are completely selfless, without assuming the rapid decay property. In particular, our main theorems yield numerous new examples of simple, monotracial $\mathrm{C}^{\ast}$-algebras with strict comparison, stable rank one, and admitting a unique unital embedding of the Jiang--Su algebra $\mathcal{Z}$ up to approximate unitary equivalence, and of purely infinite $\mathrm{C}^{\ast}$-algebras in the traceless case.

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arXiv2025

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

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.

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arXiv2024

Continuous actions on primitive ideal spaces lift to $\mathrm{C}^{\ast}$-actions

We prove that for any second-countable, locally compact group $G$, any continuous $G$-action on the primitive ideal space of a separable, nuclear $\mathrm{C}^{\ast}$-algebra $B$ such that $B \cong B\otimes\mathcal{K}\otimes\mathcal{O}_2$ is induced by an action on $B$. As a direct consequence, we establish that every continuous action on the primitive ideal space of a separable, nuclear $\mathrm{C}^{\ast}$-algebra is induced by an action on a $\mathrm{C}^{\ast}$-algebra with the same primitive ideal space. Moreover, we discuss an application to the classification of equivariantly $\mathcal{O}_2$-stable actions.

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arXiv2023

Classification of equivariantly $\mathcal{O}_2$-stable amenable actions on nuclear $\mathrm{C}^\ast$-algebras

Given a second-countable, locally compact group $G$, we consider amenable $G$-actions on separable, stable, nuclear $\mathrm{C}^\ast$-algebras that are isometrically shift-absorbing and tensorially absorb the trivial action on the Cuntz algebra $\mathcal{O}_2$. We show that such actions are classified up to cocycle conjugacy by the induced $G$-action on the primitive ideal space. In the special case when $G$ is exact, we prove a unital version of our classification theorem. For compact groups, we obtain a classification up to conjugacy.

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