2 3 Ja n 20 01 Fredholm modules over certain group C
نویسنده
چکیده
In this article we consider examples of Fredholm modules over the group C*-algebras of the infinite dihedral and discrete Heisenberg groups. In the first case we exhibit sufficient Fredholm modules to generate the entire K-homology of the algebra. We then turn our attention to the six term cyclic exact sequence in K-homology for a crossed product by Z dual to the Pimsner-Voiculescu sequence for K-theory. We calculate explicitly the boundary morphisms for this sequence, which are given by taking the Kasparov product with the KK-element corresponding to the Pimsner-Voiculescu " Toeplitz " extension, and illustrate this with examples, in particular the noncommutative tori.
منابع مشابه
ar X iv : m at h / 06 01 47 2 v 1 [ m at h . Q A ] 1 9 Ja n 20 06 REPRESENTATIONS OF QUANTUM GROUPS DEFINED OVER COMMUTATIVE RINGS II
In this article we study the structure of highest weight modules for quantum groups defined over a commutative ring with particular emphasis on the structure theory for invariant bilinear forms on these modules.
متن کاملBounded noncommutative geometry and boundary actions of hyperbolic groups
We use the canonical Lipschitz geometry available on the boundary of a hyperbolic group to construct finitely summable Fredholm modules over the crossed product of the boundary action. The procedure yields a full set of representatives of the K-homology of the crossed product, and all of them are p-summable for p in an appropriate range related to the geometry of the boundary. By restricting th...
متن کامل. R A ] 1 2 Ja n 20 01 INTRODUCTION TO A - INFINITY ALGEBRAS AND MODULES
These are expanded notes of four introductory talks on A∞-algebras, their modules and their derived categories.
متن کاملOn nest modules of matrices over division rings
Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...
متن کاملFredholm Modules over Certain Group C*-algebras
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 Z×σZ2 and the semidirect product group Z×σZ. We present a unified treatment of the K-homology and cyclic cohomology of these algebras.
متن کامل