Simple subquotients of crossed products by abelian groups and twisted group algebras

Siegfried Echterhoff

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arXiv · 2601.14097

Simple subquotients of crossed products by abelian groups and twisted group algebras

Siegfried Echterhoff

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Abstract

Motivated by work of Poguntke we study the question under what conditions simple subquotients of crossed products $A\rtimes_{\alpha}G$ by (twisted) actions of abelian groups $G$ are isomorphic to simple twisted group algebras of abelian groups. As a consequence, we recover a theorem of Poguntke's saying that the simple subquotients of group $C^*$-algebras of connected groups are either stably isomorphic to $\mathbb C$ or they are stably isomorphic to simple non-commutative tori.

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BibTeX RIS

Siegfried Echterhoff. 2026-01-20. Simple subquotients of crossed products by abelian groups and twisted group algebras. https://arxiv.org/abs/2601.14097

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