quantum metric spaces — 1 articles found.

A Survey of the Preservation of Symmetries by the Dual Gromov-Hausdorff Propinquity

C. R. Math. Rep. Acad. Sci. Canada Vol. 40 (3) 2018, pp. 65-90
Vol.40 (3) 2018
Frederic Latremoliere Details
(Received: 2018-05-05 , Revised: 2018-05-05 )
(Received: 2018-05-05 , Revised: 2018-05-05 )

Frederic Latremoliere,Department of Mathematics, University of Denver, Denver CO 80208; e-mail: frederic@math.du.edu

Abstract/Résumé:

We survey the symmetry preserving properties for the dual propinquity, under natural non-degeneracy and equicontinuity conditions. These properties are best formulated using the notion of the covariant propinquity when the symmetries are encoded via the actions of proper monoids and groups. We explore the issue of convergence of Cauchy sequences for the covariant propinquity, which captures, via a compactness result, the fact that proper monoid actions can pass to the limit for the dual propinquity.

Nous étudions les propriétés de conservation des symmétries des espaces quantiques pour la proximité duale, sous des conditions naturelles d’équicontinuité et de non dégénérescence. Ces propriétés sont exprimées naturellement dans le language de la proximité covariante, qui permet de discuter la convergence d’actions de groupes et semigroupes sur les espaces quantiques. Nous explorons le problème de la convergence des suites de Cauchy pour la proximité covariante, qui capture, grâce a un théoreme de compacité, le fait que les actions de monoides propres passent à la limite pour la proximité duale.

Keywords: C*-dynamical systems, Gromov-Hausdor convergence, Gromov-Hausdor distance for proper monoids, Lip-norms, Monge- Kantorovich distance, Noncommutative metric geometry, proper monoids, quantum metric spaces

AMS Subject Classification: K-theory and operator algebras -including cyclic theory, Noncommutative geometry (__ la Connes) 46L80, 58B34

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