Metrics on states from actions of compact groups

Abstract

Let a compact Lie group act ergodically on a unital $C^{\ast }$-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-$\ast$ topology.

Publication version. Very minor corrections. 20 pages AMSTEX

References in corpus (3)

• Gravity coupled with matter and foundation of non-commutative geometry
• Morita equivalence and duality
• An Introduction to K-theory and Cyclic Cohomology

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