arXiv subjects

Alexander G. Ravnanger

Publications and source records attributed to Alexander G. Ravnanger.

2 recordsLinked to original sources

arXiv2026

On AF- and type I-ideals in certain crossed product C$^\ast$-algebras

We study locally finite-dimensional ideals in crossed products of totally disconnected spaces by free actions of the integers and in uniform Roe algebras of exact discrete groups. In the first case, we present a dynamical description of the largest locally finite-dimensional ideal, which turns out to coincide with the intersection of all maximal ideals. In the latter case, we provide a coarse geometric characterization of the locally finite-dimensional compact ideals. Moreover, we show that for crossed products of totally disconnected spaces by free actions of exact groups, the largest type I-ideal is locally finite-dimensional. In the case of uniform Roe algebras, we provide coarse geometric conditions for compact ideals guaranteeing that the ideal is type I and admits an embedding of a UHF-algebra, respectively.

math.OA↗

arXiv2025

On Fourier and Fourier-Stieltjes Algebras of C$^\ast$-Dynamical Systems

We continue the study of the Fourier-Stieltjes algebra of a C$^\ast$-dynamical system, initiated by Bédos and Conti, and recently extended by Buss, Kwaśniewski, McKee and Skalski. Firstly, we introduce and study a natural notion of a Fourier algebra of a C$^\ast$-dynamical system. Notably, we show that it can be equivalently defined as the closure of the multipliers with finite support or as the closure of multipliers coming from regular equivariant representations. Secondly, we undertake an analysis of the equivariant representation theory of commutative systems. Our main result about this is a description of the group theoretical aspect of the equivariant representation theory in terms of cocycle representations of the underlying transformation group.

math.OA↗