A uniqueness theorem for twisted groupoid C*-algebras

B Armstrong - Journal of Functional Analysis, 2022 - Elsevier
We present a uniqueness theorem for the reduced C*-algebra of a twist E over a Hausdorff
étale groupoid G. We show that the interior IE of the isotropy of E is a twist over the interior IG …

C⁎-algebras of extensions of groupoids by group bundles

M Ionescu, A Kumjian, JN Renault, A Sims… - Journal of Functional …, 2021 - Elsevier
Given a normal subgroup bundle A of the isotropy bundle of a groupoid Σ, we obtain a
twisted action of the quotient groupoid Σ/A on the bundle of group C⁎-algebras determined …

Analyzing the Weyl construction for dynamical Cartan subalgebras

A Duwenig, E Gillaspy, R Norton - International Mathematics …, 2022 - academic.oup.com
When the reduced twisted-algebra of a non-principal groupoid admits a Cartan subalgebra,
Renault's work on Cartan subalgebras implies the existence of another groupoid description …

Semigroups of self-similar actions and higher rank Baumslag-Solitar semigroups

R Valente, D Yang - arXiv preprint arXiv:2405.07062, 2024 - arxiv.org
In this paper, we initiate the study of higher rank Baumslag-Solitar semigroups and their
related C*-algebras. We focus on two extreme, but interesting, classes-one is related to …

Smooth Cartan triples and Lie twists over Hausdorff\'etale Lie groupoids

A Duwenig, A Sims - arXiv preprint arXiv:2309.09177, 2023 - arxiv.org
We characterise when a smooth structure on the unit space of a Hausdorff\'etale groupoid
can be extended to a Lie-groupoid structure on the whole groupoid. We introduce Lie twists …

Nontraditional models of -Cartan pairs

JH Brown, E Gillaspy - arXiv preprint arXiv:2309.06539, 2023 - arxiv.org
This paper explores the tension between multiple models and rigidity for groupoid $ C^* $-
algebras. We begin by identifying $\Gamma $-Cartan subalgebras $ D $ inside twisted …

Fourier coefficients and rapid decay in reduced groupoid C*-algebras

AH Fuller, P Karmakar - arXiv preprint arXiv:2412.05410, 2024 - arxiv.org
Let $\Sigma\rightarrow G $ be a twist over a locally compact Hausdorff\'{e} tale groupoid $ G
$. Given $ f $ in the reduced C $^* $-algebra $ C_r^*(\Sigma; G) $ with open support …

The Zappa-Sz\'{e} p product of twisted groupoids

A Duwenig, B Li - arXiv preprint arXiv:2406.00466, 2024 - arxiv.org
We define and study the external and the internal Zappa-Sz\'{e} p product of twists over
groupoids. We determine when a pair $(\Sigma_ {1},\Sigma_ {2}) $ of twists over a matched …

A twist over a minimal\'etale groupoid that is topologically nontrivial over the interior of the isotropy

B Armstrong, A Ng, A Sims, Y Zhou - arXiv preprint arXiv:2312.08683, 2023 - arxiv.org
A twist over a minimal étale groupoid that is topologically nontrivial over the interior of the
isotropy Page 1 A TWIST OVER A MINIMAL ÉTALE GROUPOID THAT IS TOPOLOGICALLY …

Non-traditional Cartan subalgebras in twisted groupoid C*-algebras

A Duwenig, DP Williams, J Zimmerman - arXiv preprint arXiv:2403.15255, 2024 - arxiv.org
Well-known work of Renault shows that if $\mathcal {E} $ is a twist over a second countable,
effective,\'etale groupoid $ G $, then there is a naturally associated Cartan subalgebra of the …