Related papers: Negative resolution to the $C^*$-algebraic Tarski …

We obtain a characterization of the unital C*-algebras with the property that every element is a limit of products of positive elements, thereby answering a question of Murphy and Phillips.

We demonstrate that pure C*-algebras form a robust class by proving that pureness follows from very weak comparison and divisibility properties. Using this, we show that every simple, non-elementary C*-algebra with a unique quasitrace and…

We provide some background on the category of classifiable $\mathrm{C}^*$-algebras, whose objects are infinite-dimensional, simple, separable, unital $\mathrm{C}^*$-algebras that have finite nuclear dimension and satisfy the universal…

Let $\ell$ be a length function on a group G, and let $M_{\ell}$ denote the operator of pointwise multiplication by $\ell$ on $\bell^2(G)$. Following Connes, $M_{\ell}$ can be used as a ``Dirac'' operator for $C_r^*(G)$. It defines a…

Complexity rank for $C^*$-algebras was introduced by the second author and Yu for applications towards the UCT: very roughly, this rank is at most $n$ if you can repeatedly cut the $C^*$-algebra in half at most $n$ times, and end up with…

We compute the topological K-theory of the group C*-algebra C*_r(G) for a group extension Z^n->G->Z/m provided that the conjugation action of Z/m on Z^n is free outside the origin.

For every $p\geq 2$, we give a characterization of positive definite functions on a free group with finitely many generators, which can be extended to the positive linear functionals on the free group $C^*$-algebra associated with the ideal…

In this note, we derive some consequences of the von Neumann algebra uniqueness theorems developed in a previous paper (see arXiv:1207.6741v1). In particular, 1) we solvein a paper of Futamura, Kataoka, and Kishimoto, by proving that if A…

We construct the first example of a $C^*$-algebra $A$ with the properties in the title. This gives a new example of non-nuclear $A$ for which there is a unique $C^*$-norm on $A \otimes A^{op}$. This example is of particular interest in…

We consider the properties weak cancellation, K_1-surjectivity, good index theory, and K_1-injectivity for the class of extremally rich C*-algebras, and for the smaller class of isometrically rich C*-algebras. We establish all four…

Exotic group $C^*$-algebras are $C^*$-algebras that lie between the universal and the reduced group $C^*$-algebra of a locally compact group. We consider simple Lie groups $G$ with real rank one and investigate their exotic group…

Let \( m, n \in \mathbb{N}_0 \), and let \( X \) be a closed subset of \( \mathbb{T}^{\binom{m+n}{2}} \). We define \( C^{m,n}_X \) to be the universal \( C^* \)-algebra among those generated by \( m \) unitaries and \( n \) isometries…

In this paper, we introduce a notion of a self-similar action of a group $G$ on a $k$-graph $\Lambda$, and associate it a universal C*-algebra $\O_{G,\Lambda}$. We prove that $\O_{G,\Lambda}$ can be realized as the Cuntz-Pimsner algebra of…

We introduce strong Morita equivalence for inverse semigroups. This notion encompasses Mark Lawson's concept of enlargement. Strongly Morita equivalent inverse semigroups have Morita equivalent universal groupoids in the sense of Paterson…

We show that the $C^*$-algebra associated by Nekrashevych to a contracting self-similar group is simple if and only if the corresponding complex $\ast$-algebra is simple. We also improve on Steinberg and Szaka\'c's algorithm to determine if…

We survey the results required to pass between full and reduced coactions of locally compact groups on C*-algebras, which say, roughly speaking, that one can always do so without changing the crossed-product C*-algebra. Wherever possible we…

This paper characterizes the unital C*-algebra generated by a single invertible element as the unital free product of C[0,1] and C(T). To do this, I develop techniques to split and merge presentations of C*-algebras using free products in…

Using the Baum-Connes conjecture with coefficients, we develop a K-theory formula for reduced C*-algebras of strongly $0$-$E$-unitary inverse semigroups, or equivalently, for certain reduced partial crossed products. In the case of…

As a generalization of the Exel-Pardo's notion of self-similar graph, we introduce self-similar group actions on ultragraphs and their $C^*$-algebras. We then approach to the $C^*$-algebras by inverse semigroup and tight groupoid models.

We determine the class of finite T_0-spaces allowing for a universal coefficient theorem computing equivariant KK-theory by filtrated K-theory.