Metrics on states from actions of compact groups

Details Metrics on states from actions of compact groups Metrics on states from actions of compact groups

1998-07-16

arxiv.org/abs/math/9807084v2

Documenta Mathematica 3 (1998) 215-229

Mathematics

Operator Algebras

Publication version. Very minor corrections. 20 pages AMSTEX

Scientific paper

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.

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