Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weakly Symmetric Pseudo-Riemannian Nilmanifolds   In an earlier paper we developed the classification of weakly symmetric
pseudo--riemannian manifolds $G/H$ where $G$ is a semisimple Lie group and $H$
is a reductive subgroup. We derived the classification from the cases where $G$
is compact. As a consequence we obtained the classification of semisimple
weakly symmetric manifolds of Lorentz signature $(n-1,1)$ and trans--lorentzian
signature $(n-2,2)$. Here we work out the classification of weakly symmetric
pseudo--riemannian nilmanifolds $G/H$ from the classification for the case $G =
N\rtimes H$ with $H$ compact and $N$ nilpotent. It turns out that there is a
plethora of new examples that merit further study. Starting with that
riemannian case, we see just when a given involutive automorphism of $H$
extends to an involutive automorphism of $G$, and we show that any two such
extensions result in isometric pseudo--riemannian nilmanifolds. The results are
tabulated in the last two sections of the paper.

11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci