Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1804.08015

Bundles of Generalized Fixed-Point Algebras for Proper Groupoid Dynamical Systems

Jonathan H. Brown·Leonard T. Huang
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, we show that the generalized fixed-point algebra of a proper groupoid dynamical system, under certain assumptions, may be fibered over any locally compact Hausdorff space to which a continuous map exists from the unit space of the underlying groupoid. We will also provide some important examples.

Explore related subjects

math.OAmath.DSmath.FA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jonathan H. Brown, Leonard T. Huang. 2018-04-21. Bundles of Generalized Fixed-Point Algebras for Proper Groupoid Dynamical Systems. https://arxiv.org/abs/1804.08015

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

KEEP EXPLORING

Related papers

arXiv2026

$C^*$-extreme maps and $*$-homomorphisms from $C(X)$ to finite von Neumann algebras

Given a unital inclusion of $C^*$-algebras $\mathcal C \subset \mathcal A$ and a unital inclusion $\mathcal C \subset \mathcal B$ into a von Neumann algebra $\mathcal B$, we investigate the extreme points of unital completely positive maps from $\mathcal A$ to $\mathcal B$ that fix $\mathcal C$ denoted by $UCP_\mathcal C(\mathcal A, \mathcal B)$. This space is obviously convex and $C^*$-convex with respect to the $C^*$-algebra $\mathcal C' \cap \mathcal B$. In this article we show that the $\mathcal C' \cap \mathcal B$-extreme points are exactly the $*$-homomorphisms that fix $\mathcal C$ when $\mathcal A$ is commutative and $\mathcal B$ has a normal faithful center valued trace. This generalizes a result due to Farenick and Morenz where $\mathcal C = \mathbb C 1$ and $\mathcal B = M_n(\mathbb C)$.

math.OA↗
arXiv2026

Quantum Cheeger Inequalities for KMS-Symmetric Quantum Markov Semigroups

In this paper, we establish a quantum Cheeger inequality for primitive KMS-symmetric quantum Markov semigroups in terms of projection conductance. We discuss both projection conductance and classical conductance for graph-based KMS-symmetric quantum Markov semigroups. We show that hypercontractivity and the logarithmic Sobolev inequality hold for primitive KMS-symmetric quantum Markov semigroups. We also present applications of the quantum Cheeger inequality to logarithmic Sobolev inequalities, hypercontractivity, and complete modified logarithmic Sobolev inequalities.

math.OA↗
arXiv2026

A characterization of simplicity of reduced groupoid C*-algebras

We show that, for a second-countable locally compact Hausdorff étale minimal groupoid with compact unit space, simplicity of the reduced groupoid C*-algebra implies the existence of a comeager set of unit points with C*-simple isotropy group. Combining this result with work of Christensen and Neshveyev on exotic completions of isotropy group algebras, we show that the converse implication is also true. Finally, we construct a Hausdorff étale minimal groupoid with an isotropy group whose induced exotic completion differs from its reduced group C*-algebra, answering a question of Christensen and Neshveyev.

math.OA↗