Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Internal symmetry of the $L_{\leqslant 3}$ algebra arising from a Lie
  pair   A Lie pair is an inclusion $A$ to $L$ of Lie algebroids over the same base
manifold. In an earlier work, the third author with Bandiera, Sti\'{e}non, and
Xu introduced a canonical $L_{\leqslant 3}$ algebra $\Gamma(\wedge^\bullet
A^\vee)\otimes \Gamma(L/A)$ whose unary bracket is the Chevalley-Eilenberg
differential arising from every Lie pair $(L,A)$. In this note, we prove that
to such a Lie pair there is an associated Lie algebra action by
$\mathrm{Diff}(L)$ on the $L_{\leqslant 3}$ algebra $\Gamma(\wedge^\bullet
A^\vee)\otimes \Gamma(L/A)$. Here $\mathrm{Diff}(L)$ is the space of
$1$-differentials on the Lie algebroid $L$, or infinitesimal automorphisms of
$L$. The said action gives rise to a larger scope of gauge equivalences of
Maurer-Cartan elements in $\Gamma(\wedge^\bullet A^\vee)\otimes \Gamma(L/A)$,
and for this reason we elect to call the $\mathrm{Diff}(L)$-action internal
symmetry of $\Gamma(\wedge^\bullet A^\vee)\otimes \Gamma(L/A)$.

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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: stat