Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local rigidity for actions of Kazhdan groups on non commutative
  $L_p$-spaces   Given a discrete group $\Gamma$, a finite factor $\mathcal N$ and a real
number $p\in [1, +\infty)$ with $p\neq 2,$ we are concerned with the rigidity
of actions of $\Gamma$ by linear isometries on the $L_p$-spaces $L_p(\mathcal
N)$ associated to $\mathcal N$. More precisely, we show that, when $\Gamma$ and
$\mathcal N$ have both Property (T) and under some natural ergodicity
condition, such an action $\pi$ is locally rigid in the group $G$ of linear
isometries of $L_p(\mathcal N)$, that is, every sufficiently small perturbation
of $\pi$ is conjugate to $\pi$ under $G$. As a consequence, when $\Gamma$ is an
ICC Kazhdan group, the action of $\Gamma$ on its von Neumann algebra ${\mathcal
N}(\Gamma)$, given by conjugation, is locally rigid in the isometry group of
$L_p({\mathcal N}(\Gamma)).$

36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat