Projective representations on operator algebras

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.

arXiv commentMinor changes. Accepted version. Rev. Mat. Iberoam., to appear