Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reynolds $n$-Lie algebras and NS-$n$-Lie algebras   In this paper, first we introduce the notion of a Reynolds operator on an
$n$-Lie algebra and illustrate the relationship between Reynolds operators and
derivations on an $n$-Lie algebra. We give the cohomology theory of Reynolds
operators on an $n$-Lie algebra and study infinitesimal deformations of
Reynolds operators using the second cohomology group. Then we introduce the
notion of NS-$n$-Lie algebras, which are generalizations of both $n$-Lie
algebras and $n$-pre-Lie algebras. We show that an NS-$n$-Lie algebra gives
rise to an $n$-Lie algebra together with a representation on itself. Reynolds
operators and Nijenhuis operators on an $n$-Lie algebra naturally induce
NS-$n$-Lie algebra structures. Finally, we construct Reynolds $(n+1)$-Lie
algebras and Reynolds $3$-Lie algebras from Reynolds $n$-Lie algebras and
Reynolds commutative associative algebras respectively.

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The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th