Related papers: On quantales that classify C*-algebras

We study $C^*$-algebras arising from $C^*$-correspondences, which was introduced by the author. We prove the gauge-invariant uniqueness theorem, and obtain conditions for our $C^*$-algebras to be nuclear, exact, or satisfy the Universal…

We show that nuclear C*-algebras have a refined version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use…

Let $A$ be a unital $C^*$-algebra. Its unitary group, $UA$, contains a wealth of topological information about $A$. However, the homotopy type of $UA$ is out of reach even for $A = M_2(\CC)$. There are two simplifications which have been…

Let $C^*(\cls)$ be the $C^*$ algebra generated by an operator system $\cls$ i.e. a unital $*$-closed subspace of a unital $C^*$ algebra $\cla$. We prove that any complete order isomorphism $\cli:\cls \raro \cls'$ between two such operator…

In this note we include two remarks about bounded ($\underline{not}$ necessarily contractive) linear projections on a von Neumann-algebra. We show that if $M$ is a von Neumann-subalgebra of $B(H)$ which is complemented in B(H) and…

For each natural number $n$, we define a category whose objects are discriminant algebras in rank $n$, i.e. functorial means of attaching to each rank-$n$ algebra a quadratic algebra with the same discriminant. We show that the discriminant…

It is shown that topological freeness of Rieffel's induced representation functor implies that any $C^*$-algebra generated by a faithful covariant representation of a Hilbert bimodule $X$ over a $C^*$-algebra $A$ is canonically isomorphic…

A bivariant functor is defined on a category of *-algebras and a category of operator ideals, both with actions of a second countable group $G$, into the category of abelian monoids. The element of the bivariant functor will be…

Let $p\in(1,\infty)\backslash\{2\}$. We show that every homomorphism from a $C^{*}$-algebra $\mathcal{A}$ into $B(l^{p}(J))$ satisfies a compactness property where $J$ is any set. As a consequence, we show that a $C^{*}$-algebra…

We describe a method for associating a $C^{*}$-correspondence to a Mauldin-Williams graph and show that the Cuntz-Pimsner algebra of this $C^{*}$-correspondence is isomorphic to the $C^{*}$-algebra of the underlying graph. In addition, we…

Quantum field theory in curved spacetime may be defined either through a manifestly unitary canonical approach or via the manifestly covariant path integral formalism. For gauge theories, these two approaches have produced conflicting…

Let $\gamma = (\gamma_1,...,\gamma_N)$, $N \geq 2$, be a system of proper contractions on a complete metric space. Then there exists a unique self-similar non-empty compact subset $K$. We consider the union ${\mathcal G} = \cup_{i=1}^N…

Algebraic actions of unipotent groups $U$ actions on affine $k-$varieties $X$ ($k$ an algebraically closed field of characteristic 0) for which the algebraic quotient $X//U$ has small dimension are considered$.$ In case $X$ is factorial,…

A universal coefficient theorem is proved for C*-algebras over an arbitrary finite T_0-space X which have vanishing boundary maps. Under bootstrap assumptions, this leads to a complete classification of unital/stable real-rank-zero…

We study C*-algebras generated by two partitions of unity with orthogonality relations governed by hypercubes $Q_n$ for $n \in \mathbb{N} \setminus \{0\}$. These "hypercube C*-algebras'' are special cases of bipartite graph C*-algebras…

Given C*-algebras A and B and an imprimitivity A-B-bimodule X, we construct an explicit isomorphism X_* : K_i(A) --> K_i(B) where K_i denote the complex K-theory functors for i=0, 1. Our techniques do not require separability nor existence…

For a given unitary operator $U$ on a separable complex Hilbert space $\h$, we describe the set $\mathscr{C}_{c}(U)$ of all conjugations $C$ (antilinear, isometric, and involutive maps) on $\h$ for which $C U C = U$. As this set might be…

We formalize eight different notions of isomorphism among (unital) graph C*-algebras, and initiate the study of which of these notions may be described geometrically as generated by moves. We propose a list of seven types of moves that we…

For elements $a, b$ of a C*-algebra we denote $a=ab$ by $a\ll b$. We show that all $\omega_1$-unital C*-algebras have $\ll$-increasing approximate units, extending a classical result for $\sigma$-unital C*-algebras. We also construct (in…

A unitary equivalence class of endomorphisms of a unital C$^{*}$-algebra ${\cal A}$ is called a {\it sector} of ${\cal A}$. We introduced permutative endomorphisms of the Cuntz algebra ${\cal O}_N$ in the previous work. Branching laws of…