15 citations · 41 across the 14 of their papers we have counts for
17 papers
A unified approach for classifying simple nuclear -algebras
Ben Bouwen, James Gabe
We provide a new proof of the Kirchberg--Phillips theorem by adapting the framework laid out by Carrión--Gabe--Schafhauser--Tikuisis--White for classifying separable simple unital…
Self-adjoint traces on the Pedersen ideal of -algebras
James Gabe, Alistair Miller
In order to circumvent a fundamental issue when studying densely defined traces on -algebras -- which we refer to as the Trace Question -- we initiate a systematic…
Classifying -homomorphisms I: Unital simple nuclear -algebras
José R. Carrión, James Gabe, Christopher Schafhauser +2
We classify the unital embeddings of a unital separable nuclear -algebra satisfying the universal coefficient theorem into a unital simple separable nuclear -algebra that…
The dynamical Kirchberg-Phillips theorem
James Gabe, Gábor Szabó
Let be a second-countable, locally compact group. In this article we study amenable -actions on Kirchberg algebras that admit an approximately central embedding of a canonic…
Dynamic asymptotic dimension and Matui's HK conjecture
Christian Bönicke, Clément Dell'Aiera, James Gabe +1
We prove that the homology groups of a principal ample groupoid vanish in dimensions greater than the dynamic asymptotic dimension of the groupoid (as a side-effect of our methods,…
Classification of -stable -algebras
James Gabe
I present a proof of Kirchberg's classification theorem: two separable, nuclear, -stable -algebras are stably isomorphic if and only if they are ideal-re…