Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some characterizations of Hom-Leibniz algebras   Some basic properties of Hom-Leibniz algebras are found. These properties are
the Hom-analogue of corresponding well-known properties of Leibniz algebras.
Considering the Hom-Akivis algebra associated to a given Hom-Leibniz algebra,
it is observed that the Hom-Akivis identity leads to an additional property of
Hom-Leibniz algebras, which in turn gives a necessary and sufficient condition
for Hom-Lie admissibility of Hom-Leibniz algebras. A necessary and sufficient
condition for Hom-power associativity of Hom-Leibniz algebras is also found.

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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th