76 citations · 782 across the 86 of their papers we have counts for
105 papers
The crystal groupoid of a compact semisimple Lie group and its flag varieties
Aidan Sims, Robert Yuncken
We introduce the crystal groupoid of a compact semisimple Lie group ; it is the Deaconu-Renault groupoid of a higher-rank analogue of a subshift of finite type on an inverse lim…
Global and local triviality for extensions of ample groupoids: an algebraic approach
Nathan Brownlowe, Lisa Orloff Clark, Enrique Pardo +1
Using the duality between the categories of inverse semigroups and ample groupoids, we prove the triviality (global and local) of the central term of the extension in terms of twis…
Embeddability of higher-rank graphs in groupoids, and the structure of their C*-algebras
Nathan Brownlowe, Alex Kumjian, David Pask +1
We show that the C*-algebra of a row-finite source-free k-graph is Rieffel-Morita equivalent to a crossed product of an AF algebra by the fundamental group of the k-graph. When the…
Smooth Cartan triples and Lie twists over Hausdorff étale Lie groupoids
Anna Duwenig, Aidan Sims
We describe how to recover a Lie structure on a twist over a Hausdorff étale groupoid from functional-analytic data in the spirit of Connes' reconstruction theorem for manifolds. W…
Ideal structure of C*-algebras of commuting local homeomorphisms
Kevin Aguyar Brix, Toke Meier Carlsen, Aidan Sims
We determine the primitive ideal space and hence the ideal lattice of a large class of separable groupoid C*-algebras that includes all 2-graph C*-algebras. A key ingredient is the…
KK-duality for self-similar groupoid actions on graphs
Nathan Brownlowe, Alcides Buss, Daniel Gonçalves +3
We extend Nekrashevych's -duality for -algebras of regular, recurrent, contracting self-similar group actions to regular, contracting self-similar groupoid actions on a gr…