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arXiv · 1811.06424

Complex group rings and group C*-algebras of group extensions

Johan Öinert·Stefan Wagner
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Abstract

Let $N$ and $H$ be groups, and let $G$ be an extension of $H$ by $N$. In this article we describe the structure of the complex group ring of $G$ in terms of data associated with $N$ and $H$. In particular, we present conditions on the building blocks $N$ and $H$ guaranteeing that $G$ satisfies the zero-divisor and idempotent conjectures. Moreover, for central extensions involving amenable groups we present conditions on the building blocks guaranteeing that the Kadison-Kaplansky conjecture holds for the group C*-algebra of $G$.

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Johan Öinert, Stefan Wagner. 2018-11-15. Complex group rings and group C*-algebras of group extensions. https://arxiv.org/abs/1811.06424

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