Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reality Properties of Conjugacy Classes in G_2   Let $G$ be an algebraic group over a field $k$. We call $g\in G(k)$ {\bf
real} if $g$ is conjugate to $g^{-1}$ in $G(k)$. In this paper we study reality
for groups of type $G_2$ over fields of characteristic different from 2. Let
$G$ be such a group over $k$. We discuss reality for both semisimple and
unipotent elements. We show that a semisimple element in $G(k)$ is real if and
only if it is a product of two involutions in $G(k)$. Every unipotent element
in $G(k)$ is a product of two involutions in $G(k)$. We discuss reality for
$G_2$ over special fields and construct examples to show that reality fails for
semisimple elements in $G_2$ over $\Q$ and $\Q_p$. We show that semisimple
elements are real for $G_2$ over $k$ with $cd(k)\leq 1$. We conclude with
examples of nonreal elements in $G_2$ over $k$ finite, with characteristic $k$
not 2 or 3, which are not semisimple or unipotent.

12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph