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

2007/07/21 by Charlotte Wahl, Wahl, Charlotte
Mathematics · #19K53 #46L55 #58J22 #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.KT #math.OA #msc:19K53 #msc:46L55 #msc:58J22

paper · pdf · doi:10.48550/arxiv.0707.3207

22 pages; sign corrections in section 4 and 5

arxiv created 2008/06/28 · arxiv updated 2009/12/01

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.

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