156 citations · 468 across the 30 of their papers we have counts for
34 papers
Regular simple nuclear C*-algebras
Samuel Evington, Shanshan Hua, Christopher Schafhauser +3
We prove Z-stability for all simple, separable, pure, nuclear C*-algebras. Combining this with very recent work of Thiel completes the proof of the Toms-Winter conjecture. We do th…
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.
Etale equivalence relations with certain prescribed torsion in their homology
Michael Francesco Ala, Hung-Chang Liao, Aaron Tikuisis
Given a non-cyclic simple dimension group D and a subgroup E of Q/Z, we produce a minimal étale equivalence relation R such that H_0(\R) is isomorphic to D \oplus E, where H_0(R) d…
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…
Corrigendum to "K-theoretic characterization of C*-algebras with approximately inner flip"
Dominic Enders, André Schemaitat, Aaron Tikuisis
An error in the original paper is identified and corrected. The C*-algebras with approximately inner flip, which satisfy the UCT, are identified (and turn out to be fewer than what…
Polar decomposition in algebraic K-theory
Pawel Sarkowicz, Aaron Tikuisis
We show that the Hausdorffized algebraic K-theory of a C*-algebra decomposes naturally as a direct sum of the Hausdorffized unitary algebraic K-theory and the space of continuous a…
The nuclear dimension of extensions of commutative C*-algebras by the compact operators
Ruaridh Gardner, Aaron Tikuisis
Generalizing the case of the Toeplitz algebra by Brake and Winter, we prove that the nuclear dimension of a C*-algebra extension of C(X) by the compact operators is equal to the di…
Classifying maps into uniform tracial sequence algebras
Jorge Castillejos, Samuel Evington, Aaron Tikuisis +1
We classify -homomorphisms from nuclear -algebras into uniform tracial sequence algebras of nuclear -stable -algebras via tracial data.
Almost finiteness, comparison, and tracial -stability
Hung-Chang Liao, Aaron Tikuisis
Inspired by Kerr's work on topological dynamics, we define tracial -stability for sub--algebras. We prove that for a countable discrete amenable group acting…
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…
Nuclear dimension of simple C*-algebras
Jorge Castillejos, Samuel Evington, Aaron Tikuisis +2
We compute the nuclear dimension of separable, simple, unital, nuclear, Z-stable C*-algebras. This makes classification accessible from Z-stability and in particular brings large c…
Maximally unitarily mixed states on a C*-algebra
Robert Archbold, Leonel Robert, Aaron Tikuisis
We investigate the set of maximally mixed states of a C*-algebra, extending previous work by Alberti on von Neumann algebras. We show that, unlike for von Neumann algebras, the set…
Relative commutant pictures of Roe algebras
Jan Spakula, Aaron Tikuisis
Let X be a proper metric space, which has finite asymptotic dimension in the sense of Gromov (or more generally, straight finite decomposition complexity of Dranishnikov and Zarich…
The Dixmier property and tracial states for C*-algebras
Robert Archbold, Leonel Robert, Aaron Tikuisis
It is shown that a unital C*-algebra A has the Dixmier property if and only if it is weakly central and satisfies certain tracial conditions. This generalises the Haagerup-Zsido th…
Rohklin dimension for C*-correspondences
N. P. Brown, A. Tikuisis, A. M. Zelenberg
We extend the notion of Rokhlin dimension from topological dynamical systems to -correspondences. We show that in the presence of finite Rokhlin dimension and a mild quasidiag…
Quasidiagonality of nuclear C*-algebras
Aaron Tikuisis, Stuart White, Wilhelm Winter
We prove that faithful traces on separable and nuclear C*-algebras in the UCT class are quasidiagonal. This has a number of consequences. Firstly, by results of many hands, the cla…
Corrigendum to "Regularity for stably projectionless, simple C*-algebras"
Henning Petzka, Aaron Tikuisis
An error is identified and corrected in the construction of a non-Z-stable, stably projectionless, simple, nuclear C*-algebra carried out in a paper by the second author.
Covering dimension of C*-algebras and 2-coloured classification
Joan Bosa, Nathanial P. Brown, Yasuhiko Sato +3
We introduce the concept of finitely coloured equivalence for unital *-homomorphisms between C*-algebras, for which unitary equivalence is the 1-coloured case. We use this notion t…
Decomposition rank of approximately subhomogeneous C*-algebras
George A. Elliott, Zhuang Niu, Luis Santiago +1
It is shown that every Jiang-Su stable approximately subhomogeneous C*-algebra has finite decomposition rank. Previously, it was not even known that such algebras have finite nucle…
Relative commutants of strongly self-absorbing C*-algebras
Ilijas Farah, Bradd Hart, Mikael Rørdam +1
The relative commutant of a strongly self-absorbing algebra is indistinguishable from its ultrapower . This applies both to the case w…
High-dimensional Z-stable AH algebras
Aaron Tikuisis
It is shown that a C*-algebra of the form C(X,U), where U is a UHF algebra, is not an inductive limit of subhomogeneous C*-algebras of topological dimension less than that of X. Th…