Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $L_\infty$-deformations of associative Rota-Baxter algebras and
  homotopy Rota-Baxter operators   A relative Rota-Baxter algebra is a triple $(A, M, T)$ consisting of an
algebra $A$, an $A$-bimodule $M$, and a relative Rota-Baxter operator $T$.
Using Voronov's derived bracket and a recent work of Lazarev et al., we
construct an $L_\infty [1]$-algebra whose Maurer-Cartan elements are precisely
relative Rota-Baxter algebras. By a standard twisting, we define a new
$L_\infty [1]$-algebra that controls Maurer-Cartan deformations of a relative
Rota-Baxter algebra $(A,M,T)$. We introduce the cohomology of a relative
Rota-Baxter algebra $(A, M, T)$ and study infinitesimal deformations in terms
of this cohomology (in low dimensions). As an application, we deduce cohomology
of coboundary skew-symmetric infinitesimal bialgebras and discuss their
infinitesimal deformations. Finally, we define homotopy relative Rota-Baxter
operators and find their relationship with homotopy dendriform algebras and
homotopy pre-Lie algebras.

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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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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: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an