Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 0705.3919

On the Structure of Some Reduced Amalgamated Free Product C*-Algebras

Nikolay A. Ivanov
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study some reduced free products of C*-algebras with amalgamations. We give sufficient conditions for the positive cone of the K_0 group to be the largest possible. We also give sufficient conditions for simplicity and uniqueness of trace. We use the later result to give a necessary and sufficient condition for simplicity and uniqueness of trace of the reduced C*-algebras of the Baumslag-Solitar groups BS(m,n).

Explore related subjects

math.OAmath.FA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Nikolay A. Ivanov. 2007-09-04. On the Structure of Some Reduced Amalgamated Free Product C*-Algebras. https://arxiv.org/abs/0705.3919

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

KEEP EXPLORING

Related papers

arXiv2026

Simplicity of reduced crossed products

We characterize the simplicity of reduced crossed product C*-algebras in terms of stabilizer subgroups. Specifically, we prove that if $G$ is a countable group and $X$ is a minimal $G$-flow, then the reduced crossed product C*-algebra $\mathrm{C}(X) \times_λG$ is simple if and only if there is a point in $X$ with a C*-simple stabilizer subgroup. Further, these conditions are equivalent to a generic point in $X$ having a C*-simple stabilizer subgroup. We also provide an example demonstrating that this result does not extend to uncountable groups. This completely resolves a question of Ozawa.

math.OA↗
arXiv2026

$\mathrm{C}^*$-selflessness of vigorous groups

We prove that countable groups which admit a faithful piecewise minimal-extremely-proximal action on the Cantor set are $\mathrm{C}^*$-selfless. In particular, topological full groups of second countable, Hausdorff, minimal, purely infinite, topologically principal, ample groupoids with compact unit spaces are $\mathrm{C}^*$-selfless. Examples include the Higman--Thompson groups and the Brin--Thompson groups.

math.OA↗
arXiv2026

A computable wandering and tracelike vector for modular orbits in the Bergman space

We construct a function $Φ$ such that the orbit under the representation of PSL(2,Z) is an orthonormal basis for the Bergman space with weight $α=12$. Moreover, we show that $Φ$ is effectively computable as a holomorphic function on the upper half-plane (in the precise sense of computable analysis), by providing an effective procedure. This constructs a wandering and tracelike vector for PSL(2,Z), whose abstract existence was proved by Sir Vaughan Jones in his last paper, where the corresponding construction was left as a problem. The function is built using an orthonormalization and modularization method, and it displays modular reminiscencies, despite not being modular itself. provides a computable implementing vector for the abstract anti-isomorphism between the von Neumann algebra $M_{12}(Γ)$ and its commutant, which is generated, in Rădulescu's sense, by cusp-form Toeplitz operators, while Voiculescu's results provide a random matrix model for $M_{12}(Γ)$.

math.OA↗