50 citations · 115 across the 13 of their papers we have counts for
16 papers
Structure theory and stable rank for C*-algebras of finite higher-rank graphs
David Pask, Adam Sierakowski, Aidan Sims
We study the structure and compute the stable rank of C*-algebras of finite higher-rank graphs. We completely determine the stable rank of the C*-algebra when the k-graph either co…
Graded -theory and -homology of relative Cuntz-Pimsner algebras and graph -algebras
Quinn Patterson, Adam Sierakowski, Aidan Sims +1
We establish exact sequences in -theory for graded relative Cuntz-Pimsner algebras associated to nondegenerate -correspondences. We use this to calculate the graded -th…
An algebraic analogue of Exel-Pardo C*-algebras
Roozbeh Hazrat, David Pask, Adam Sierakowski +1
We introduce an algebraic version of the Katsura -algebra of a pair of integer matrices and an algebraic version of the Exel-Pardo -algebra of a self-similar action…
On the geometry of idempotents in von Neumann algebras
Thierry Giordano, Adam Sierakowski
We consider the general linear group as an invariant of von Neumann factors. We prove that up to complement, a set consisting of all idempotents generating the same right ideal adm…
Unbounded quasitraces, stable finiteness and pure infiniteness
David Pask, Adam Sierakowski, Aidan Sims
We prove that if A is a σ-unital exact C*-algebra of real rank zero, then every state on K_0(A) is induced by a 2-quasitrace on A. This yields a generalisation of Rainone's work on…
Purely infinite simple C*-algebras that are principal groupoid C*-algebras
Jonathan H. Brown, Lisa Orloff Clark, Adam Sierakowski +1
From a suitable groupoid G, we show how to construct an amenable principal groupoid whose C*-algebra is a Kirchberg algebra which is KK-equivalent to C*(G). Using this construction…
Filling families and strong pure infiniteness
Eberhard Kirchberg, Adam Sierakowski
We introduce filling families with matrix diagonalization as a refinement of the work by Rørdam and the first named author. As an application we improve a result on local pure infi…
Real rank and topological dimension of higher rank graph algebras
David Pask, Adam Sierakowski, Aidan Sims
We study dimension theory for the -algebras of row-finite -graphs with no sources. We establish that strong aperiodicity - the higher-rank analogue of condition (K) - for a…
Purely infinite -algebras associated to étale groupoids
Jonathan Brown, Lisa Orloff Clark, Adam Sierakowski
Let be a Hausdorff, étale groupoid that is minimal and topologically principal. We show that is purely infinite simple if and only if all the nonzero positive elemen…
Twisted k-graph algebras associated to Bratteli diagrams
David Pask, Adam Sierakowski, Aidan Sims
Given a system of coverings of k-graphs, we show that the cohomology of the resulting (k+1)-graph is isomorphic to that of any one of the k-graphs in the system. We then consider B…
The general linear group as a complete invariant for C*-algebras
Thierry Giordano, Adam Sierakowski
In 1955 Dye proved that two von Neumann factors not of type I_2n are isomorphic (via a linear or a conjugate linear *-isomorphism) if and only if their unitary groups are isomorphi…
Strong pure infiniteness of crossed products
Eberhard Kirchberg, Adam Sierakowski
Consider an exact action of discrete group on a separable -algebra . It is shown that the reduced crossed product is strongly purely infinite - prov…
Purely infinite partial crossed products
Thierry Giordano, Adam Sierakowski
Let (A,G,α) be a partial dynamical system. We show that there is a bijective correspondence between G-invariant ideals of A and ideals in the partial crossed product A xr G provide…
K-theory of certain purely infinite crossed products
G. A. Elliott, A. Sierakowski
It was shown by Rordam and the second named author that a countable group G admits an action on a compact space such that the crossed product is a Kirchberg algebra if, and only if…
Purely infinite C*-algebras arising from crossed products
Mikael Rordam, Adam Sierakowski
We study conditions that will ensure that a crossed product of a C*-algebra by a discrete exact group is purely infinite (simple or non-simple). We are particularly interested in t…
The ideal structure of reduced crossed products
Adam Sierakowski
Let (A,G) be a C*-dynamical system with G discrete. In this paper we investigate the ideal structure of the reduced crossed product C*-algebra and in particular we determine suffic…