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 …
related C*-algebras. We focus on two extreme, but interesting, classes-one is related to …
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 …
algebras. We begin by identifying $\Gamma $-Cartan subalgebras $ D $ inside twisted …
The Zappa-Sz\'{e} p product of twisted groupoids
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 …
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
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 …
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 …
effective,\'etale groupoid $ G $, then there is a naturally associated Cartan subalgebra of the …
Pushouts of extensions of groupoids by bundles of abelian groups
We analyse extensions $\Sigma $ of groupoids $ G $ by bundles $ A $ of abelian groups.
We describe a pushout construction for such extensions, and use it to describe the extension …
We describe a pushout construction for such extensions, and use it to describe the extension …