Projective representations on operator algebras

Sergio Girón Pacheco

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arXiv · 2510.02924

Projective representations on operator algebras

Sergio Girón Pacheco

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Abstract

We establish new restrictions for the values of the 2 cohomology lifting obstruction for projective unitary representations of second countable, locally compact Hausdorff groups on operator algebras. Using these, we show that every projective representation on the Jiang--Su algebra lifts to a genuine group representation. We also characterise the possible values of lifting obstructions for finite group projective representations on UHF-algebras of infinite type and Cuntz algebras. Finally, we show that certain 2-cocycles of Property (T) groups cannot arise as lifting invariants of projective representations on the hyperfinite II$_{1}$ factor.

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BibTeX RIS

Sergio Girón Pacheco. 2025-10-03. Projective representations on operator algebras. https://arxiv.org/abs/2510.02924

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