Related papers: $C^{*}$-algebras isomorphically representable on $…

Motivated by advances in categorical probability, we introduce non-commutative almost everywhere (a.e.) equivalence and disintegrations in the setting of C*-algebras. We show that C*-algebras (resp. W*-algebras) and a.e. equivalence classes…

Given a locally compact quantum group $\mathbb G$, we study the structure of completely bounded homomorphisms $\pi:L^1(\mathbb G)\rightarrow\mathcal B(H)$, and the question of when they are similar to $\ast$-homomorphisms. By analogy with…

We examine the question of when the *-homomorphism of full amalgamated free product C*-algebras \lambda: A *_D B --> A' *_{D'} B', arising from compatible inclusions of C*-algebras A in A', B in B' and D in D', is an embedding. Results…

We study the general form of isomorphisms on the algebra of compactly supported complex-valued continuous functions defined on a locally compact Hausdorff space (the proof of which works for the algebra of $C^k-$differentiable functions on…

Given a directed graph $E$ and a labeling $\mathcal{L}$, one forms the labeled graph $C^*$-algebra by taking a weakly left--resolving labeled space $(E, \mathcal{L}, \mathcal{B})$ and considering a universal generating family of partial…

We give a classification result for a certain class of $C^{*}$-algebras $\mathfrak{A}$ over a finite topological space $X$ in which there exists an open set $U$ of $X$ such that $U$ separates the finite and infinite subquotients of…

Let $F$ be a fixed field of characteristic zero containing an element $i$ such that $i^2 = -1$. In this paper we consider finite dimensional superalgebras over $F$ endowed with a pseudoautomorphism $p$ and we investigate the asymptotic…

We show that there exists a completely bounded (c.b. in short) homomorphism $u$ from a $C^*$-algebra $C$ with the lifting property (in short LP) into a QWEP von Neumann algebra $N$ that is not strongly similar to a $*$-homomorphism, i.e.…

If A is a C*-algebra, G a locally compact group, K{\subset}G a compact subgroup and {\alpha}:G{\to}Aut(A) a continuous homomorphism, let Ax_{{\alpha}}G denote the crossed product. In this paper we prove that Ax_{{\alpha}}G is nuclear…

A C*-algebra is determined to a great extent by the partial order of its commutative C*-algebras. We study order-theoretic properties of this dcpo. Many properties coincide: the dcpo is, equivalently, algebraic, continuous, meet-continuous,…

We show that certain pullbacks of $*$-algebras equivariant with respect to a compact group action remain pullbacks upon completing to $C^*$-algebras. This unifies a number of results in the literature on graph algebras, showing that…

Let $\mathbb F$ be an algebraically closed field, $G$ be an abelian group, and let $A$ and $B$ be arbitrary finite-dimensional $G$-graded simple algebras over $\mathbb F$. We prove that $A$ and $B$ are isomorphic if, and only if, they…

We show that there is a one-to-one correspondence between compact quantum subgroups of a co-amenable locally compact quantum group $\mathbb{G}$ and certain left invariant C*-subalgebras of $C_0(\mathbb{G})$. We also prove that every compact…

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 nuclear dimension. A key step in the proof is that subhomogeneous…

Let $p$ be a prime number, let $d$ be an integer and let $G$ be a $d$-generated finite $p$-group of nilpotency class smaller than $p$. Then the number of possible isomorphism types for the mod $p$ cohomology algebra $H^*(G;{\mathbb F}_p)$…

We characterize the class of RFD $C^*$-algebras as those containing a dense subset of elements that attain their norm under a finite-dimensional representation. We show further that this subset is the whole space precisely when every…

By a labeled graph $C^*$-algebra we mean a $C^*$-algebra associated to a labeled space $(E,\mathcal L,\mathcal E)$ consisting of a labeled graph $(E,\mathcal L)$ and the smallest normal accommodating set $\mathcal E$ of vertex subsets.…

We present a generalization of H\"older duality to algebra-valued pairings via $L^p$-modules. H\"older duality states that if $p \in (1, \infty)$ and $p^{\prime}$ are conjugate exponents, then the dual space of $L^p(\mu)$ is isometrically…

We develop notions of a representation of a topological graph E and of a covariant representation of a topological graph E which do not require the machinery of C*-correspondences and Cuntz-Pimsner algebras. We show that the C*-algebra…

We study surjective homomorphisms f:\prod_I A_i\to B of not-necessarily-associative algebras over a commutative ring k, for I a generally infinite set; especially when k is a field and B is countable-dimensional over k. Our results have the…