Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The density theorem for projective representations via twisted group von
  Neumann algebras   We consider converses to the density theorem for irreducible, projective,
unitary group representations restricted to lattices using the dimension theory
of Hilbert modules over twisted group von Neumann algebras. We show that under
the right assumptions, the restriction of a $\sigma$-projective unitary
representation $\pi$ of a group $G$ to a lattice $\Gamma$ extends to a Hilbert
module over the twisted group von Neumann algebra $\text{L}(\Gamma,\sigma)$. We
then compute the center-valued von Neumann dimension of this Hilbert module.
For abelian groups with 2-cocycle satisfying Kleppner's condition, we show that
the center-valued von Neumann dimension reduces to the scalar value $d_{\pi}
\text{vol}(G/\Gamma)$, where $d_{\pi}$ is the formal dimension of $\pi$ and
$\text{vol}(G/\Gamma)$ is the covolume of $\Gamma$ in $G$. We apply our results
to characterize the existence of multiwindow super frames and Riesz sequences
associated to $\pi$ and $\Gamma$. In particular, we characterize when a lattice
in the time-frequency plane of a second countable, locally compact abelian
group admits a Gabor frame or Gabor Riesz sequence.

18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga