Related papers: Computably strongly self-absorbing C*-algebras

We show that the $\ca$-envelope of the tensor algebra of an arbitrary $\ca$-correspondence $\X$ coincides with the Cuntz-Pimsner algebra $\O_{\X}$, as defined by Katsura \cite{Ka}. This improves earlier results of Muhly and Solel and…

We consider a certain class of unital simple stably finite C^*-algebras which absorb the Jiang-Su algebra Z tensorially. Under a mild assumption, we show that the crossed product of a C^*-algebra in this class by a strongly outer action of…

We analyze the structure of co-invariant subspaces for representations of the Cuntz algebras O_N for N = 2,3,..., N < infinity, with special attention to the representations which are associated to orthonormal and tight-frame wavelets in…

We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…

We introduce a novel commutative C*-algebra $C_\mathcal{R}(X)$ of functions on a symplectic vector space $(X,\sigma)$ admitting a complex structure, along with a strict deformation quantization that maps a dense subalgebra of…

We show that every strongly $\mathbb{Z}$-graded C*-algebra (equivalently, every C*-algebra carrying a strongly continuous $\mathbb{T}$-action with full spectral subspaces) is a Cuntz--Pimsner algebra, and describe subalgebras and subspaces…

In this paper we associate to every reduced C*-algebraic quantum group A a universal C*-algebraic quantum group. We fine tune a proof of Kirchberg to show that every *-representation of a modified L1-space is generated by a unitary…

Let (G,P) be a quasi-lattice ordered group and let X be a compactly aligned product system over P of Hilbert bimodules. Under mild hypotheses we associate to X a C*-algebra which we call the Cuntz-Nica-Pimsner algebra of X. Our construction…

The universal C*-algebras of discrete product systems generalize the Toeplitz- Cuntz algebras and the Toeplitz algebras of discrete semigroups. We consider a semigroup P which is quasi-lattice ordered in the sense of Nica, and, for a…

Let X be a path connected, compact metric space and let A be a unital separable simple nuclear Z-stable real rank zero C*-algebra. We classify all the unital *-embeddings (up to approximate unitary equivalence) of C(X) into A. Specifically,…

Given an arbitrary countable ordinal $\alpha $, we introduce the notion of type $I_{\alpha }$ C*-algebra and $\alpha $-subhomogeneous C*-algebra. When $\alpha =0$, these recover the notions of Fell C*-algebra and of commutative C*-algebra,…

For special universal $C^*$-algebras associated to $k$-semigraphs we present the universal representations of these algebras, prove a Cuntz--Krieger uniqueness theorem, and compute the $K$-theory. These $C^*$-algebras seem to be the most…

In a recent paper, Pardo and the first named author introduced a class of C*-algebras which which are constructed from an action of a group on a graph. This class was shown to include many C*-algebras of interest, including all Kirchberg…

Kadison and Kastler introduced a natural metric on the collection of all C*-subalgebras of the bounded operators on a separable Hilbert space. They conjectured that sufficiently close algebras are unitarily conjugate. We establish this…

In this paper, we accomplish two objectives. Firstly, we extend and improve some results in the theory of (semi-)strongly self-absorbing C*-dynamical systems, which was introduced and studied in previous work. In particular, this concerns…

Let $\Omega$ be a class of ${\rm C^*}$-algebras. In this paper, we study a class of not necessarily unital generalized tracial approximation ${\rm C^*}$-algebras, and the class of simple ${\rm C^*}$-algebras which can be generally tracially…

We show, based on previous results, that two separable simple stably projectionless amenable ${\cal Z}$-stable $C^*$-algebras which satisfy the UCT are isomorphic if and only if they have the same Elliott invariant.

Suppose a C*-algebra A acts by adjointable operators on a Hilbert A-module X. Pimsner constructed a C*-algebra O_X which includes, for particular choices of X, crossed products of A by Z, the Cuntz algebras O_n, and the Cuntz-Krieger…

In this paper we study the C*-envelope of the (non-self-adjoint) tensor algebra associated via subproduct systems to a finite irreducible stochastic matrix $P$. Firstly, we identify the boundary representations of the tensor algebra inside…

A subalgebra $\mathcal{A}$ of $\mathbb{M}_n(\mathbb{C})$ is said to be projection compressible if $P\mathcal{A}P$ is an algebra for all orthogonal projections $P\in\mathbb{M}_n(\mathbb{C})$. Likewise, $\mathcal{A}$ is said to be idempotent…