8 papers · 1 filter
The real and stable rank of tracially complete C*-algebras
Samuel Evington, Aaron Tikuisis
We prove that a factorial tracially complete C*-algebra with CPoU has real rank zero and stable rank one. This leads to an essentially complete description of the Cuntz semigroup o…
Nuclear C*-algebras: 99 problems
Christopher Schafhauser, Aaron Tikuisis, Stuart White
We present a collection of questions related to the structure and classification of nuclear C*-algebras.
Uniform property and the small boundary property
Grigoris Kopsacheilis, Hung-Chang Liao, Aaron Tikuisis +1
We prove that, for a free action of a countably infinite discrete amenable group on a compact metric space, the small boundary property is implied by…
Tracially Complete C*-Algebras
José R. Carrión, Jorge Castillejos, Samuel Evington +4
We introduce a new class of operator algebras -- tracially complete C*-algebras -- as a vehicle for transferring ideas and results between C*-algebras and their tracial von Neumann…
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…
Uniform property Gamma
Jorge Castillejos, Samuel Evington, Aaron Tikuisis +1
We further examine the concept of uniform property Gamma for C*-algebras introduced in our joint work with Winter. In addition to obtaining characterisations in the spirit of Dixmi…