Journal of Operator Theory

Volume 63, Issue 1, Winter 2010 pp. 216-242.

Index theory for actions of compact Lie groups on $C^*$-algebras

Authors: Charlotte Wahl
Author institution: Leibniz-Forschungsstelle der Goettinger Akademie der Wissenschaften, Waterloostr. 8, 30169 Hannover, Germany

Summary: We study the index theory for actions of compact Lie groups on $C^*$-algebras with an emphasis on principal actions. Given an invariant semifinite faithful trace on the $C^*$-algebra we get semifinite spectral triples. For circle actions we consider the relation to the dual Pimsner--Voiculescu sequence. On the way we show that the notions `saturated'' and `principal'' are equivalent for actions by compact Lie groups.

Keywords: $C^*$-dynamical system, index theory, principal, saturated, KK-theory, spectral triple

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