Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Realizations of globally exceptional $\mathbb{Z}_2 \times \mathbb{Z}_2$-
  symmetric spaces   A classification is given of the exceptional $\mathbb{Z}_2 \times
\mathbb{Z}_2$-symmetric spaces $G/K$ by A.Kollross, where $G$ is an exceptional
compact Lie group or $S\!pin(8)$, and moreover the structure of $K$ is
determined as Lie algebra. In the present article, we give a pair of commuting
involutive automorphisms (involutions) $\tilde{\sigma}, \tilde{\tau}$ of $G$
concretely and determine the structure of group $G^{\sigma} \cap G^{\tau}$
corresponding to Lie algebra $\mathfrak{g}^\sigma \cap \mathfrak{g}^\tau$,
where $G$ is an exceptional compact Lie group. Thereby, we realize exceptional
$\mathbb{Z}_2 \times \mathbb{Z}_2$-symmetric spaces, globally.

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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-fin