Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nijenhuis algebras, NS algebras and N-dendriform algebras   In this paper we study (associative) Nijenhuis algebras, with emphasis on the
relationship between the category of Nijenhuis algebras and the categories of
NS algebras. This is in analogy to the well-known theory of the adjoint functor
from the category of Lie algebras to that of associative algebras, and the more
recent results on the adjoint functor from the categories of dendriform and
tridendriform algebras to that of Rota-Baxter algebras. We first give an
explicit construction of free Nijenhuis algebras and then apply it to obtain
the universal enveloping Nijenhuis algebra of an NS algebra. We further apply
the construction to determine the binary quadratic nonsymmetric algebra, called
the N-dendriform algebra, that is compatible with the Nijenhuis algebra. As it
turns out, the N-dendriform algebra has more relations than the NS algebra.

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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol