Related papers: Metrics on states from actions of compact groups
In this survey article, we present some panorama of groups acting on metric spaces of non-positive curvature. We introduce the main examples and their rigidity properties , we show the links between algebraic or analytic properties of the…
We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite nor transitive. We discuss various topological and…
We discuss the problem of deciding when a metrisable topological group $G$ has a canonically defined local Lipschitz geometry. This naturally leads to the concept of minimal metrics on $G$, that we characterise intrinsically in terms of a…
We describe an algorithm that constructs a list of all topological types of holomorphic actions of a finite group on a compact Riemann surface $C$ of genus at least $g \geq 2$ with $C/G \cong \mathbb{P}^1$.
We study meromorphic actions of unipotent complex Lie groups on compact K\"ahler manifolds using moment map techniques. We introduce natural stability conditions and show that sets of semistable points are Zariski-open and admit geometric…
The C*-envelope of the limit algebra (or limit space) of a contractive regular system of digraph algebras (or digraph spaces) is shown to be an approximately finite C*-algebra and the direct system for the C*-envelope is determined…
In this paper the metric on the set of mixing actions of a countable infinite group is introduced so that the corresponding space is complete and separable. Keywords and phrases. Monotilable group, measure preserving transformations, mixing…
We introduce the notion of stationary actions in the context of C*-algebras. We develop the basics of the theory, and provide applications to several ergodic theoretical and operator algebraic rigidity problems.
In this paper, we employ operator system techniques to investigate structural properties of C*-algebras. In particular, we provide more direct proofs of results concerning exactness and the local lifting property (LLP) of group…
We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotients of different representations and…
We construct an analogue of the classical $L^p$-Wasserstein distance for the state space of a $C^*$-algebra. Given an abstract Lipschitz gauge on a $C^*$-algebra $\mathcal{A}$ in the sense of Rieffel, one can define the classical…
Three properness conditions for actions of locally compact groups on C*-algebras are studied, as well as their dual analogues for coactions. To motivate the properness conditions for actions, the commutative cases (actions on spaces) are…
The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…
We use a tensor C*-category with conjugates and two quasitensor functors into the category of Hilbert spaces to define a *-algebra depending functorially on this data. If one of them is tensorial, we can complete in the maximal C*-norm. A…
In this article we define a metric on C(S1; S1). Also, we give some density results in C(S^1; S^1).
Given a topological graph $E$, we give a complete description of tracial states on the C*-algebra $\mathrm{C}^*(E)$ which are invariant under the gauge action; there is an affine homeomorphism between the space of gauge invariant tracial…
We geometrically describe the relation induced on a set of graphs by isomorphism of their associated graph C*-algebras as the smallest equivalence relation generated by five types of moves. The graphs studied have finitely many vertices and…
A collection of partial isometries whose range and initial projections satisfy a specified set of conditions often gives rise to a partial representation of a group. The C*-algebra generated by the partial isometries is thus a quotient of…
The existence of kinematic formulas for area measures with respect to any connected, closed subgroup of the orthogonal group acting transitively on the unit sphere is established. In particular, the kinematic operator for area measures is…
We prove that the space $\mathscr{P}(\mathfrak{A})$ of pure states of a nonelementary, simple, separable, real rank zero $C^*$-algebra $\mathfrak{A}$ has trivial homotopy groups of all orders when $\mathscr{P}(\mathfrak{A})$ is equipped…