Let a compact Lie group act ergodically on a unital -algebra . We consider several ways of using this structure to define metrics on the state space of . 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.
Cite this article
Marc A. Rieffel, Metrics on states from actions of compact groups. Doc. Math. 3 (1998), pp. 215–230DOI 10.4171/DM/41