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…
The nuclear dimension of -stable -algebras
Joan Bosa, James Gabe, Aidan Sims +1
We show that every nuclear -stable *-homomorphism with a separable exact domain has nuclear dimension at most 1. In particular separable, nuclear, $\mathcal O_\i…
The unital Ext-groups and classification of -algebras
James Gabe, Efren Ruiz
The semigroups of unital extensions of separable -algebras come in two flavours: a strong and a weak version. By the unital -groups, we mean the groups of inv…
Traceless AF embeddings and unsuspended -theory
James Gabe
I show that quasidiagonality and AF embeddability are equivalent properties for traceless -algebras and are characterised in terms of the primitive ideal space. For…
A new proof of Kirchberg's -stable classification
James Gabe
I present a new proof of Kirchberg's -stable classification theorem: two separable, nuclear, stable/unital, -stable -algebras are isomorphic if…
Quasidiagonal traces on exact -algebras
James Gabe
Recently, it was proved by Tikuisis, White and Winter that any faithful trace on a separable, nuclear -algebras in the UCT class is quasidiagonal. Building on their work, w…
Lifting theorems for completely positive maps
James Gabe
We prove lifting theorems for completely positive maps going out of exact -algebras, where we remain in control of which ideals are mapped into which. A consequence is, tha…
Absorbing representations with respect to closed operator convex cones
James Gabe, Efren Ruiz
We initiate the study of absorbing representations of -algebras with respect to closed operator convex cones. We completely determine when such absorbing representations ex…
A note on non-unital absorbing extensions
James Gabe
Elliott and Kucerovsky stated that a non-unital extension of separable -algebras with a stable ideal, is nuclearly absorbing if and only if the extension is purely large. H…
K-theory for Leavitt path algebras: computation and classification
James Gabe, Efren Ruiz, Mark Tomforde +1
We show that the long exact sequence for K-groups of Leavitt path algebras deduced by Ara, Brustenga, and Cortinas extends to Leavitt path algebras of countable graphs with infinit…
Classification of tight -algebras over the one-point compactification of
James Gabe, Efren Ruiz
We prove a strong classification result for a certain class of -algebras with primitive ideal space , where is the one-point…
Graph -algebras with a primitive ideal space
James Gabe
We give necessary and sufficient conditions which a graph should satisfy in order for its associated -algebra to have a primitive ideal space. We give a description o…