46 citations · 194 across the 26 of their papers we have counts for
30 papers
Cartan inverse semigroups and twisted Steinberg algebras
Nathan Brownlowe, Lisa Orloff Clark, Ying-Fen Lin +1
We introduce the notion of a Cartan inverse semigroup and an (algebraic) semi-Cartan subalgebra in an -algebra A, providing a purely algebraic analogue of Cartan semigroups and…
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…
Tubular partitions and representations of the quantum automorphism group of a homogeneous rooted tree
Nathan Brownlowe, David Robertson
We introduce the rigid tensor category of tubular partitions, and use it to provide a combinatorial model for the representation category of the quantum automorphism group of a hom…
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…
Group actions on multitrees and the -theory of their crossed products
Nathan Brownlowe, Jack Spielberg, Anne Thomas +1
We study group actions on multitrees, which are directed graphs in which there is at most one directed path between any two vertices. In our main result we describe a six-term exac…
Self-similar quantum groups
Nathan Brownlowe, David Robertson
We introduce the notion of self-similarity for compact quantum groups. For a finite set , we introduce a -algebra , which is the quantum automorphism group of…