Z-stability of twisted group C*-algebras of nilpotent groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917510398345216 |
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| author | Enstad, Ulrik Vilalta, Eduard |
| author_facet | Enstad, Ulrik Vilalta, Eduard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18088 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Z-stability of twisted group C*-algebras of nilpotent groups Enstad, Ulrik Vilalta, Eduard Operator Algebras Functional Analysis Primary 46L05, Secondary 22E27, 42C15, 43A70, 46L08 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. |
| title | Z-stability of twisted group C*-algebras of nilpotent groups |
| topic | Operator Algebras Functional Analysis Primary 46L05, Secondary 22E27, 42C15, 43A70, 46L08 |
| url | https://arxiv.org/abs/2503.18088 |