E. Vilalta

activity

20242026

collaborators

8 papers

math.OA2026

Z-stability of twisted group C*-algebras of nilpotent groups

Ulrik Enstad, Eduard Vilalta

We prove that the twisted group C*-algebra of a finitely generated nilpotent group is $Z$ -stable if and only if it is nowhere scattered, a condition that we characterize…

math.OA2026

Strict comparison for twisted group C*-algebras

Sven Raum, Hannes Thiel, Eduard Vilalta

We prove that any reduced twisted group C*-algebra of a selfless group with the rapid decay property is selfless. As an application, we show that twisted group C*-algebras of acyli…

math.OA2026

Continuous functions over a pure C*-algebra

Apurva Seth, Eduard Vilalta

Let $X$ be a compact metric space, and let $A$ be a pure $C^{*}$ -algebra. We show that $C (X, A)$ is pure whenever $A$ is simple; or every quotient of $A$ is stably finite (e.…

math.OA2025

Centrally pure C*-algebras

Francesc Perera, Hannes Thiel, Eduard Vilalta

We show that a separable C*-algebra $A$ is $Z$ -stable if and only if its uncorrected central sequence algebra $A^{'} \cap A_{U}$ is pure, if and only if Kirchberg'…

math.OA2025

An introduction to the Global Glimm Problem

Eduard Vilalta

The Global Glimm Problem lies at the heart of several open questions regarding regularity properties of C*-algebras. The problem has been open for over two decades, and has recentl…

math.OA2025

The Global Glimm Property for C*-algebras of topological dimension zero

Ping Wong Ng, Hannes Thiel, Eduard Vilalta

We show that a C*-algebra with topological dimension zero has the Global Glimm Property (every hereditary subalgebra contains an almost full nilpotent element) if and only if it is…