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

Abstract

We study the index theory for actions of compact Lie groups on C*-algebras with an emphasis on principal actions. Given an invariant semifinite trace on the C*-algebra we obtain 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.

arXiv comment22 pages; sign corrections in section 4 and 5

References in corpus (5)

• Higher rank graph C*-algebras
• Metrics on states from actions of compact groups
• Notes on Compact Quantum Groups
• Noncommutative Geometry Approach to Principal and Associated Bundles
• Homological index formulas for elliptic operators over C*-algebras

Cited by in corpus (7)

• Index theory for locally compact noncommutative geometries
• A construction of finite index C*-algebra inclusions from free actions of compact quantum groups
• Spectral triples for noncommutative solenoidal spaces from self-coverings
• On the Chern-Gauss-Bonnet Theorem and Conformally Twisted Spectral Triples for $C^{\ast }$-Dynamical Systems
• Part I, Free Actions of Compact Abelian Groups on C*-Algebras
• Lifting spectral triples to noncommutative principal bundles
• An Atiyah Sequence for Noncommutative Principal Bundles