相关论文: Order-unit quantum Gromov-Hausdorff distance
We develop a matricial version of Rieffel's Gromov-Hausdorff distance for compact quantum metric spaces within the setting of operator systems and unital C*-algebras. Our approach yields a metric space of ``isometric'' unital complete order…
We introduce a new quantum Gromov-Hausdorff distance between C*-algebraic compact quantum metric spaces. Because it is able to distinguish algebraic structures, this new distance fixes a weakness of Rieffel's quantum distance. We show that…
By a quantum metric space we mean a C^*-algebra (or more generally an order-unit space) equipped with a generalization of the Lipschitz seminorm on functions which is defined by an ordinary metric. We develop for compact quantum metric…
Marc Rieffel had introduced the notion of the quantum Gromov-Hausdorff distance on compact quantum metric spaces and found a sequence of matrix algebras that converges to the space of continuous functions on $2$-sphere in this distance. One…
We introduce the quantum Gromov-Hausdorff propinquity, a new distance between quantum compact metric spaces, which extends the Gromov-Hausdorff distance to noncommutative geometry and strengthens Rieffel's quantum Gromov-Hausdorff distance…
We show that for any co-amenable compact quantum group A=C(G) there exists a unique compact Hausdorff topology on the set EA of isomorphism classes of ergodic actions of G such that the following holds: for any continuous field of ergodic…
We provide a detailed study of actions of the integers on compact quantum metric spaces, which includes general criteria ensuring that the associated crossed product algebra is again a compact quantum metric space in a natural way. We…
We show that Rieffel's quantum Gromov-Hausdorff distance between two compact quantum metric spaces is not equivalent to the ordinary Gromov-Hausdorff distance applied to the associated state spaces.
We introduce an analogue for Lip-normed operator systems of the second author's order-unit quantum Gromov-Hausdorff distance and prove that it is equal to the first author's complete distance. This enables us to consolidate the basic theory…
A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel's Lip-norm. We develop for quantized metric spaces an operator space version of quantum Gromov-Hausdorff distance. We show that two…
Precipitating a notion emerging from recent research, we formalise the study of a special class of compact quantum metric spaces. Abstractly, the additional requirement we impose on the underlying order unit spaces is the Riesz…
We introduce a hypertopology, induced by an inframetric up to full quantum isometry, on the class of pointed proper quantum metric spaces, which are separable, possibly non-unital, C*-algebras endowed with an analogue of the Lipschitz…
Metric noncommutative geometry, initiated by Alain Connes, has known some great recent developments under the impulsion of Rieffel and the introduction of the category of compact quantum metric spaces topologized thanks to the quantum…
We investigate a q-deformation of the arc length metric on the unit circle. This q-deformation arises naturally from the Dirac operator by replacing the standard integers by their q-deformed analogues. Nonetheless, we show that the…
Over the last 25 years, the notion of "fuzzy spaces" has become ubiquitous in the high-energy physics literature. These are finite dimensional noncommutative approximations of the algebra of functions on a classical space. The most well…
Given a compact metric space X and a unital C*-algebra A, we introduce a family of seminorms on the C*-algebra of continuous functions from X to A, denoted C(X, A), induced by classical Lipschitz seminorms that produce compact quantum…
We present a survey of the dual Gromov-Hausdorff propinquity, a noncommutative analogue of the Gromov-Hausdorff distance which we introduced to provide a framework for the study of the noncommutative metric properties of C*-algebras. We…
We prove that all the compact metric spaces are in the closure of the class of full matrix algebras for the quantum Gromov-Hausdorff propinquity. We also show that given an action of a compact metrizable group G on a quasi-Leibniz compact…
The statement that one can approximate a quantum torus by some twisted convolution C*-algebra of a (finite) quotient of Z^d can be found in the physics literature dealing with quantum field theory and M-theory. In this paper, we show that…
An action of a compact quantum group on a compact metric space $(X,d)$ is (D)-isometric if the distance function is preserved by a diagonal action on $X\times X$. We show that an isometric action in this sense has the following additional…