Journal of Operator Theory

Volume 51, Issue 1, Winter 2004 pp. 141-160.

Fredholm modules over certain group $C^*$-algebras

Authors: Tom Hadfield
Author institution: Department of Mathematics, University College, Cork, Ireland

Summary: Motivated by the search for new examples of ``noncommutative manifolds'', we study the noncommutative geometry of the group $C^*$-algebras of various discrete groups. The examples we consider are the infinite dihedral group ${\bbb Z} {\times_{\sigma}} {\bbb Z}_2$ and the semidirect product group ${\bbb Z} {\times_{\sigma}} {\bbb Z}$. We present a unified treatment of the {\rm K}-homology and cyclic cohomology of these algebras.

Keywords: Noncommutative geometry, K-homology, group $C^*$-algebra

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