Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.36459

Classification of reduced free products of nuclear C*-algebras

George A. Elliott·Chun Guang Li·Zhuang Niu
View original source ↗Read source document ↗Export metadata ↓

Abstract

Consider the countably infinite reduced free product $D$ of copies of $(\mathrm C([0,1]),λ)$, where $λ$ is Lebesgue measure. It is proved that finite and countable reduced free products of unital separable nuclear UCT $\mathrm C^*$-algebras with respect to a chosen family of faithful traces are classified, after adjoining $D$, by the Elliott invariant. In other words, an isomorphism between the naive K-theory invariants of two such algebras is induced by an isomorphism between the algebras.

Explore related subjects

math.OA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

George A. Elliott, Chun Guang Li, Zhuang Niu. 2026-10-27. Classification of reduced free products of nuclear C*-algebras. https://arxiv.org/abs/2610.36459

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

On the embedding rigidity problem for uniformly locally finite coarse spaces

In this paper, we construct countable uniformly locally finite metric spaces $X$ and $Y$ such that $C_u^*(X)$ is isomorphic to a hereditary $C^*$-subalgebra of $C_u^*(Y)$, but neither space coarsely embeds into the other. This gives a negative answer to the embedding rigidity problem for uniformly locally finite coarse spaces. On the positive side, we prove that a hereditary embedding $C_u^*(X)\to C_u^*(Y)$ implies an injective coarse embedding $X\to Y$ whenever $C_u^*(Y)$ contains no block-rank-one ghost projection. In particular, this strengthens the coarse embedding theorem of Braga, Farah, and Vignati by obtaining injectivity under the same hypothesis that every sparse subspace of $Y$ yields only compact ghost projections.

math.OA↗
arXiv2026

C*-algebras of groupoid morphisms

In this paper we suggest a definition for a C*-algebra attached to an injective morphism of some Étale groupoid. We take into account all the peculiarities of such objects and present some interesting relations with already well-known C*-algebras from the literature.

math.OA↗
arXiv2026

$\mathcal{W}$-absorbing actions of finite groups on the Razak-Jacelon algebra

We say that a countable discrete group action $α$ on a C$^*$-algebra $A$ is \textit{$\mathcal{W}$-absorbing} if there exist a C$^*$-algebra $B$ and an action $β$ on $B$ such that $α$ is cocycle conjugate to $β\otimes \mathrm{id}_{\mathcal{W}}$ on $B\otimes \mathcal{W}$ where $\mathcal{W}$ is the Razak-Jacelon algebra. In this paper, we completely classify outer $\mathcal{W}$-absorbing actions of finite groups on $\mathcal{W}$ up to conjugacy and cocycle conjugacy.

math.OA↗