Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification problem of simple Hom-Lie algebras   First, we construct some families of nonsolvable anticommutative algebras,
solvable Lie algebras and even nilpotent Lie algebras, that can be endowed with
the structure of simple Hom-Lie algebras. This situation shows that a
classification of simple Hom-Lie algebras would be unrealistic without any
further restrictions. Therefore, we introduce the class of \emph{strongly
simple Hom-Lie algebras}, which is the class of anticommutative algebras that
are simple Hom-Lie with respect to all their twisting maps. We show some of its
properties, provide a characterisation and explore some of its subclasses.
Then, we classify completely regular simple Hom-Lie algebras over any arbitrary
field. Furthermore, we establish that every simple anticommutative algebra of
dimension $3$ turns out to be a simple Lie algebra where its Lie bracket is
deformed by a bijective linear map, and also we determine all the simple
Hom-Lie algebras in dimension $2$, that were wrongly claimed to be nonexistent
in \cite{CH}.

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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: physics