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arXiv · 2301.01027

Detecting ideals in reduced crossed product C*-algebras of topological dynamical systems

Are Austad·Sven Raum
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Abstract

We introduce the $\ell^1$-ideal intersection property for crossed product C*-algebras. It is implied by C*-simplicity as well as C*-uniqueness. We show that topological dynamical systems of arbitrary lattices in connected Lie groups, arbitrary linear groups over the integers in a number field and arbitrary virtually polycyclic groups have the $\ell^1$-ideal intersection property. On the way, we extend previous results on C*-uniqueness of $\mathrm{L}^1$-groupoid algebras to the general twisted setting.

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Are Austad, Sven Raum. 2023-01-03. Detecting ideals in reduced crossed product C*-algebras of topological dynamical systems. https://doi.org/10.1017/s147474802510145x

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