Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 2-graded polynomial identities for the Jordan algebra of the symmetric
  matrices of order two   The Jordan algebra of the symmetric matrices of order two over a field $K$
has two natural gradings by $\mathbb{Z}_2$, the cyclic group of order 2. We
describe the graded polynomial identities for these two gradings when the base
field is infinite and of characteristic different from 2. We exhibit bases for
these identities in each of the two cases. In one of the cases we perform a
series of computations in order to reduce the problem to dealing with
associators while in the other case one employs methods and results from
Invariant theory. Moreover we extend the latter grading to a
$\mathbb{Z}_2$-grading on $B_n$, the Jordan algebra of a symmetric bilinear
form in a vector space of dimension $n$ ($n=1$, 2, \dots, $\infty$). We call
this grading the \textsl{scalar} one since its even part consists only of the
scalars. As a by-product we obtain finite bases of the $\mathbb{Z}_2$-graded
identities for $B_n$. In fact the last result describes the weak Jordan
polynomial identities for the pair $(B_n, V_n)$.

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The categories of this paper are: chem-ph
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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: chao-dyn
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The categories of this paper are: mtrl-th
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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: q-fin
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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: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph