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arXiv · 2503.18088

Z-stability of twisted group C*-algebras of nilpotent groups

Ulrik Enstad·Eduard Vilalta
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Abstract

We prove that the twisted group C*-algebra of a finitely generated nilpotent group is $\mathcal{Z}$-stable if and only if it is nowhere scattered, a condition that we characterize in terms of the given group and 2-cocycle. As a main application, we prove new converses to the Balian-Low Theorem for projective, square-integrable representations of nilpotent Lie groups.

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Ulrik Enstad, Eduard Vilalta. 2025-03-23. Z-stability of twisted group C*-algebras of nilpotent groups. https://arxiv.org/abs/2503.18088

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