Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dendriform analogues of Lie and Jordan triple systems   We use computer algebra to determine all the multilinear polynomial
identities of degree $\le 7$ satisfied by the trilinear operations $(a \cdot b)
\cdot c$ and $a \cdot (b \cdot c)$ in the free dendriform dialgebra, where $a
\cdot b$ is the pre-Lie or the pre-Jordan product. For the pre-Lie triple
products, we obtain one identity in degree 3, and three independent identities
in degree 5, and we show that every identity in degree 7 follows from the
identities of lower degree. For the pre-Jordan triple products, there are no
identities in degree 3, five independent identities in degree 5, and ten
independent irreducible identities in degree 7. Our methods involve linear
algebra on large matrices over finite fields, and the representation theory of
the symmetric group.

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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph