Divided difference operators in equivariant KK-theory

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Let G be a compact connected Lie group with a maximal torus T. Let A, B be G-C*-algebras. We define certain divided difference operators on Kasparov's T-equivariant KK-group KKT(A, B) and show that KK G(A, B) is a direct summand of KKT(A, B). More precisely, a T-equivariant KK-class is G-equivariant if and only if it is annihilated by an ideal of divided difference operators. This result is a generalization of work done by Atiyah, Harada, Landweber and Sjamaar.

Original languageEnglish
Pages (from-to)237-261
Number of pages25
JournalJournal of Topology and Analysis
Issue number2
Publication statusPublished - Jun 2014
Externally publishedYes


  • Equivariant KK-theory
  • divided difference operators

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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