Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal Varieties and Identities of Relatively Free Algebras   Let $K$ be a field of characteristic zero and let $\mathfrak{M}_5$ be the
variety of associative algebras over $K$, defined by the identity
$[x_1,x_2][x_3,x_4,x_5]$. It is well-known that such variety is a minimal
variety and that is generated by the algebra $$A=\begin{pmatrix} E_0 & E\\ 0 &
E\\ \end{pmatrix},$$ where $E=E_0\oplus E_1$ is the Grassmann algebra. In this
paper, for any positive integer $k$, we describe the polynomial identities of
the relatively free algebras of rank $k$ of $\mathfrak{M}_5$,
\[F_k(\mathfrak{M}_5)=\dfrac{K\langle x_1,\dots, x_k \rangle}{K\langle
x_1,\dots, x_k \rangle\cap T(\mathfrak{M}_5)}.\] It turns out that such
algebras satisfy the same polynomial identities of some algebras used in the
description of the subvarieties of $\mathfrak{M}_5$, given by Di Vincenzo,
Drensky and Nardozza.

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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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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: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org