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Felipe Flores

Publications and source records attributed to Felipe Flores.

9 recordsLinked to original sources
arXiv2026

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

We present a sufficient condition for a (twisted) group action on a $\mathrm{C}^\ast$-algebra such that the corresponding reduced (twisted) group $\mathrm{C}^\ast$-algebra inclusion into the reduced (twisted) crossed product is selfless. This condition is an action-dependent version of Ozawa's $\mathrm{PHP}$ property for groups. We show that topologically free extreme boundary actions, projective actions of lattices in ${\rm PSL}(n\ge 2,\mathbb R)$, as well as certain strongly proximal actions have this property, and thus we provide examples of selfless inclusions from crossed products. As a byproduct, we also obtain that reduced (twisted) group $\mathrm{C}^\ast$-algebras of some group extensions of the form finite-by-$G$, with $G$ having the property $\mathrm{PHP}$, have stable rank one and are pure, and in particular have strict comparison. Examples include all acylindrically hyperbolic groups and all lattices in ${\rm SL}(n,\mathbb R)$ for $n\geq2$.

math.OA↗
arXiv2026

Simplicity and pure infiniteness for $\text{C}^*$-algebras associated with stabilizers of boundary actions

Given a discrete group $Γ$ acting on a compact space $X$, and a stabilizer subgroup $Λ\leq Γ$ of $X$, we use the Rieffel induction of covariant $(Λ, X)$-representations to study classes of representations induced by certain characters on $Λ$ and the $\text{C}^*$-algebras they generate. When $X$ is a $Γ$-boundary, we obtain new classes of simple, traceless group $\text{C}^*$-algebras. When the $Γ$-boundary $X$ is an extreme boundary, we show that the associated group $\text{C}^*$-algebras are also purely infinite, answering part of a question posed by Kalantar and Scarparo on $\text{C}^*$-algebras associated with Thompson's groups. The latter $\text{C}^*$-algebras are shown to be selfless in the sense of Robert.

math.OA↗
arXiv2026

Rapid decay and functional calculus in ${\rm C}^*$-probability spaces

Let $(A,ρ)$ be a tracial ${\rm C}^*$-probability space with the rapid decay property relative to a filtration $L$. We show that the associated Sobolev algebra $H_L^{\infty}(A,ρ)$ is closed under the smooth functional calculus of $A$. Some consequences include norm estimates, the ideal separation property, and the fact that the inclusion $H_L^{\infty}(A,ρ)\subset A$ induces an isomorphism in $K$-theory.

math.OA↗
arXiv2026

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.

math.OA↗
arXiv2026

Selfless inclusions arising from commensurator groups of hyperbolic groups

We provide new examples of $\mathrm{C}^*$-selfless groups and inclusions. In particular, we prove that the commensurator group ${\rm Comm}(H)$ of a torsion-free hyperbolic group $H$ is $\mathrm{C}^*$-selfless. Our approach involves showing that the Gromov boundary $\partial H$ is a topologically free extreme boundary for ${\rm Comm}(H)$, ${\rm Aut}(H)$, and for other groups that contain $H$ in an almost normal way.

math.GR↗
arXiv2025

Discrete measured groupoid von Neumann algebras via the Gaussian deformation

Given a discrete measured groupoid $\mathcal{G}$, we study properties of the corresponding von Neumann algebra $L(\mathcal{G})$ using the techniques of Popa's deformation/rigidity theory. More specifically, we define and study the Gaussian deformation associated with any $1$-cocycle of $\mathcal{G}$ and use it to prove primeness and fullness under appropriate assumptions. We also characterize the maximal rigid subalgebras of $L(\mathcal{G})$ and produce unique prime factorization results for algebras of the form $L(\mathcal{G}_1\times\ldots\times\mathcal{G}_n)$.

math.OA↗
arXiv2024

Symmetry for algebras associated to Fell bundles over groups and groupoids

To every Fell bundle $\mathscr C$ over a locally compact group ${\sf G}$ one associates a Banach $^*$-algebra $L^1({\sf G}\,\vert\,\mathscr C)$. We prove that it is symmetric whenever ${\sf G}$ with the discrete topology is rigidly symmetric. This generalizes the known case of a global action without a twist. There is also a weighted version as well as a treatment of some classes of associated integral kernels. We also deal with the case of Fell bundles over discrete groupoids. We formulate a generalization of rigid symmetry in this case and show its equivalence with an a priori stronger concept. We also study the symmetry of transformation groupoids and some permanence properties.

math.OA↗
arXiv2022

Topological Dynamics of Groupoid Actions

Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions, but which have to be put in the right setting, there are also new phenomena. Mostly for groupoids whose source map is not open (and there are many), some properties which were equivalent for group actions become distinct in this general framework; we illustrate this with various counterexamples.

math.DS↗