Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-dimensional Lie algebras of order F   $F-$Lie algebras are natural generalisations of Lie algebras (F=1) and Lie
superalgebras (F=2). When $F>2$ not many finite-dimensional examples are known.
In this paper we construct finite-dimensional $F-$Lie algebras $F>2$ by an
inductive process starting from Lie algebras and Lie superalgebras. Matrix
realisations of $F-$Lie algebras constructed in this way from
$\mathfrak{su}(n), \mathfrak{sp}(2n)$ $\mathfrak{so}(n)$ and
$\mathfrak{sl}(n|m)$, $\mathfrak{osp}(2|m)$ are given. We obtain non-trivial
extensions of the Poincar\'e algebra by In\"on\"u-Wigner contraction of certain
$F-$Lie algebras with $F>2$.

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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an