On maximal ideals in certain reduced twisted C*-crossed products

Abstract

We consider a twisted action of a discrete group G on a unital C * -algebra A and give conditions ensuring that there is a bijective correspondence between the maximal invariant ideals of A and the maximal ideals in the associated reduced C*-crossed product.

On twisted group -algebras associated with FC-hypercentral groups and other related groups

“…Motivated by Proposition 2.5, we define ICC(G) = G/F CH(G). Moreover, we let P denote the class of groups considered in [4], that consists of all PH groups [24] and of all groups satisfying property (P com ) [5]. The class P is a large subclass of the class of ICC groups, and the only amenable group belonging to P is the trivial group.…”

“…J. Packer [22] has shown that all countable nilpotent groups belong to K am (see also [26] for the case of abelian groups). Large families of nonamenable groups in K are described in [1,2,4]. We mention explicitly the class P introduced in [4], as we will refer to it later: it consists of all PH groups [24] and of all groups with property (P com ) [5].…”

“…Large families of nonamenable groups in K are described in [1,2,4]. We mention explicitly the class P introduced in [4], as we will refer to it later: it consists of all PH groups [24] and of all groups with property (P com ) [5]. In particular, all weak Powers groups [13] belong to P, and the class P contains many amalgamated free products, HNN-extensions, hyperbolic groups, Coxeter groups, and lattices in semisimple Lie groups.…”

Fourier theory andC∗-algebras

“…In a first step, one may try to describe the maximal ideals. In [7], we consider the case where the group lies in the class P consisting of all PH-groups introduced by Promislow [88] and of groups satisfying the ''combinatorial'' property (P com ) of Bekka-Cowling-de la Harpe [89]. See the diagram below for an illustration of the logical relationships between the various conditions appearing in the literature on this topic.…”

“…The presentation covers more topics than strictly needed, with the purpose of providing a reference and a source of inspiration also for future works. In Sections 2 and 3, more biased towards our own contributions [4][5][6][7][8], we present some results illustrating various aspects of Fourier theory in (possibly twisted) discrete reduced group C * -algebras and reduced C * -crossed products.…”