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arXiv · 2109.01363

$\mathcal{O}$-operators on Lie $\infty$-algebras with respect to Lie $\infty$-actions

R. Caseiro·J. Nunes da Costa
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Abstract

We define $\mathcal{O}$-operators on a Lie $\infty$-algebra $E$ with respect to an action of $E$ on another Lie $\infty$-algebra and we characterize them as Maurer-Cartan elements of a certain Lie $\infty$-algebra obtained by Voronov's higher derived brackets construction. The Lie $\infty$-algebra that controls the deformation of $\mathcal{O}$-operators with respect to a fixed action is determined.

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BibTeXRIS

R. Caseiro, J. Nunes da Costa. 2021-09-03. $\mathcal{O}$-operators on Lie $\infty$-algebras with respect to Lie $\infty$-actions. https://doi.org/10.1080/00927872.2022.2025819

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