Related papers: Strongly self-absorbing C*-dynamical systems, II

We consider group actions of topological groups on C*-algebras of the types which occur in many physics models. These are singular actions in the sense that they need not be strongly continuous, or the group need not be locally compact. We…

Let $\mathfrak{C}$ be the smallest class of countable discrete groups with the following properties: (i) $\mathfrak{C}$ contains the trivial group, (ii) $\mathfrak{C}$ is closed under isomorphisms, countable increasing unions and extensions…

Let M be a one-holed torus with boundary $\partial M$ (a circle) and $\Gamma$ the mapping class group of M fixing $\partial M$. The group $\Gamma$ acts on ${\mathcal M}_{\mathcal C}(SU(2))$ which is the space of SU(2)-gauge equivalence…

We show that the following properties of unital ${\rm C^*}$-algebra in a class of $\Omega$ are preserved by unital simple ${\rm C^*}$-algebra in the class of $\rm WTA\Omega$: $(1)$ uniform property $\Gamma$, $(2)$ a certain type of tracial…

Fell's absorption principle states that the left regular representation of a group absorbs any unitary representation of the group when tensored with it. In a weakened form, this result carries over to the left regular representation of a…

We consider an equisingularity problem for polynomial families of affine hypersurfaces $X_\tau \subset \mathbb C^n$ with (at worst) isolated singularities. We show that the constancy of the global polar invariants $\gamma^* (X_\tau)$ is…

We introduce {\it covariant structures} $\left\{(\A,\k),(\a,\aa),\(\ha,\haa\)\right\}$ formed of a separable $C^*$-algebra $\A$, a measurable twisted action $(\a,\aa)$ of the second-countable locally compact group $\G$\,, a measurable…

We show that induction of covariant representations for C*-dynamical systems is natural in the sense that it gives a natural transformation between certain crossed-product functors. This involves setting up suitable categories of…

Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…

We prove that separable, simple, unital, non-elementary, stably finite C*-algebras that have stable rank one, and that have locally finite nuclear dimension in a tracial sense, have uniform property $\Gamma$. In particular, Villadsen…

Motivated by a question of L. Robert, asking whether $\rm L(T(A)) = Lsc_{C}(T(A))$ for any separable C*-algebra A, we introduce and initiate the study of \emph{tracially reflexive C*-algebras}. We first prove that commutative C*-algebras…

Given an action by a finite quantum group $\mathbb{G}$ on a von Neumann algebra $M$, we prove that a number of familiar $W^*$ properties are equivalent for $M$ and the fixed-point algebra $M^{\mathbb{G}}$ (i.e. hold or not simultaneously…

We introduce diagonal comparison, a regularity property of diagonal pairs where the sub-C*-algebra has totally disconnected spectrum, and establish its equivalence with the concurrence of strict comparison of the ambient C*-algebra and…

In an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital $C^*$-algebras, with a particular focus on gapped maps for…

We introduce the growth rank of a C*-algebra, a (N \cup {\infty})-valued invariant which measures how far an algebra is from absorbing the Jiang-Su algebra Z tensorially. We prove that its range is exhausted by simple nuclear C*-algebras,…

Given a dynamical system $(X, \Gamma)$, the corresponding crossed product $C^*$-algebra $C(X)\rtimes_{r}\Gamma$ is called reflecting, when every intermediate $C^*$-algebra $C^*_r(\Gamma)<\mathcal{A} < C(X)\rtimes_{r}\Gamma$ is of the form…

For any unital separable simple infinite-dimensional nuclear C*-algebra with finitely many extremal traces, we prove that Z-absorption, strict comparison, and property (SI) are equivalent. We also show that any unital separable simple…

We obtain three results: 1) Every compact simplex bundle with exactly one point in the fiber over 0 is the KMS bundle of a periodic flow on the Jiang-Su algebra. 2) Let A be a separable unital C*-algebra with a unique trace state. Suppose…

Suppose that $(G,T)$ is a second countable locally compact transformation group given by a homomorphism $\ell:G\to\Homeo(T)$, and that $A$ is a separable continuous-trace \cs-algebra with spectrum $T$. An action $\alpha:G\to\Aut(A)$ is said…

We describe a systematic way of the generalization, to models with non-linear duality, of the space-time covariant and duality-invariant formulation of duality-symmetric theories in which the covariance of the action is ensured by the…