Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation of an algebra by evolution algebras   It is known that any multiplication of a finite dimensional algebra is
determined by a matrix of structural constants. In general, this is a cubic
matrix. Difficulty of investigation of an algebra depends on the cubic matrix.
Such a cubic matrix defines a quadratic mapping called an evolution operator.
In the case of evolution algebras, the cubic matrix consists many zeros
allowing to reduce it to a square matrix.
  In this paper for any finite dimensional algebra we construct a family of
evolution algebras corresponding to Jacobian of the evolution operator at a
point of the algebra. We obtain some results answering how properties of an
algebra depends on the properties of the corresponding family of evolution
algebras. Moreover, we consider evolution algebras corresponding to 2 and
3-dimensional nilpotent Leibniz algebras. We prove that such evolution algebras
are nilpotent too. Also we classify such evolution algebras.

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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: solv-int