Metrics on States from Actions of Compact Groups

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.

1991 Mathematics Subject Classification: Primary 46L87; Secondary 58B30, 60B10

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