Document Type

Article

Publication Date

10-15-2012

Keywords

Noncommutative metric geometry, Monge-Kantorovich distance, non-unital C*-algebras, Quantum Metric Spaces, Lip-norms, Moyal planes

Abstract

We introduce the notion of a quantum locally compact metric space, which is the noncommutative analogue of a locally compact metric space, and generalize to the non-unital setting the notion of quantum metric spaces introduced by Rieffel. We then provide several examples of such structures, including the Moyal plane, compact quantum metric spaces and locally compact metric spaces. This paper provides an answer to the question raised in the literature about the proper notion of a quantum metric space in the nonunital setup and offers important insights into noncommutative geometry for non compact quantum spaces.

Included in

Mathematics Commons

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