Metrics on states from actions of compact groups

1998/07/31 by Marc A. Rieffel · 3 citations
Mathematics · #math.OA #msc:46L87 #msc:58B30 #msc:60B10

paper · pdf

published as Documenta Mathematica 3 (1998) 215-229 · Publication version. Very minor corrections. 20 pages AMSTEX

arxiv created 1999/01/04 · arxiv updated 2009/11/30

Abstract

Let a compact Lie group act ergodically on a unital C^*-algebra A. We consider several ways of using this structure to define metrics on the state space of A. These ways involve length functions, norms on the Lie algebra, and Dirac operators. The main thrust is to verify that the corresponding metric topologies on the state space agree with the weak-* topology.

Cited by

• Quantum Metric Structures on Iwahori-Hecke Algebras
• Quantum Hamming Metrics
• Quantum Wasserstein distances for quantum permutation groups

Related

• Connes' metric for states in group algebras
• Group C*-algebras as compact quantum metric spaces
• Metrics on C^∗-algebras of Étale groupoids from length functions
• Group C*-algebras, metrics and an operator theoretic inequality
• Ergodic measures on compact metric spaces for isometric actions by inductively compact groups