Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Kind of Magic   We introduce the extended Freudenthal-Rosenfeld-Tits magic square based on
six algebras: the reals $\mathbb{R}$, complexes $\mathbb{C}$, ternions
$\mathbb{T}$, quaternions $\mathbb{H}$, sextonions $\mathbb{S}$ and octonions
$\mathbb{O}$. The ternionic and sextonionic rows/columns of the magic square
yield non-reductive Lie algebras, including
$\mathfrak{e}_{7\scriptscriptstyle{\frac{1}{2}}}$. It is demonstrated that the
algebras of the extended magic square appear quite naturally as the symmetries
of supergravity Lagrangians. The sextonionic row (for appropriate choices of
real forms) gives the non-compact global symmetries of the Lagrangian for the
$D=3$ maximal $\mathcal{N}=16$, magic $\mathcal{N}=4$ and magic
non-supersymmetric theories, obtained by dimensionally reducing the $D=4$
parent theories on a circle, with the graviphoton left undualised. In
particular, the extremal intermediate non-reductive Lie algebra
$\tilde{\mathfrak{e}}_{7(7)\scriptscriptstyle{\frac{1}{2}}}$ (which is not a
subalgebra of $\mathfrak{e}_{8(8)}$) is the non-compact global symmetry algebra
of $D=3$, $\mathcal{N}=16$ supergravity as obtained by dimensionally reducing
$D=4$, $\mathcal{N}=8$ supergravity with $\mathfrak{e}_{7(7)}$ symmetry on a
circle. The ternionic row (for appropriate choices of real forms) gives the
non-compact global symmetries of the Lagrangian for the $D=4$ maximal
$\mathcal{N}=8$, magic $\mathcal{N}=2$ and magic non-supersymmetric theories
obtained by dimensionally reducing the parent $D=5$ theories on a circle. In
particular, the Kantor-Koecher-Tits intermediate non-reductive Lie algebra
$\mathfrak{e}_{6(6)\scriptscriptstyle{\frac{1}{4}}}$ is the non-compact global
symmetry algebra of $D=4$, $\mathcal{N}=8$ supergravity as obtained by
dimensionally reducing $D=5$, $\mathcal{N}=8$ supergravity with
$\mathfrak{e}_{6(6)}$ symmetry on a circle.

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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex