Corpus ID: 212737155

$L_\infty$-algebra extensions of Leibniz algebras

@article{Lavau2020L\_inftyalgebraEO,
  title={\$L\_\infty\$-algebra extensions of Leibniz algebras},
  author={Sylvain Lavau and Jim Stasheff},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
Leibniz algebras have been increasingly used in gauging procedures in supergravity. Their relationship with $L_\infty$-algebras and tensor hierarchies have been explored in the physics literature. This paper is devoted to showing that a Leibniz algebra $V$ gives rise to a non-positively graded $L_\infty$-algebra. We call such an $L_\infty$-algebra an '$L_\infty$-extension of the Leibniz algebra $V$' and show that this construction is functorial. We will also use the opportunity of building this… Expand
2 Citations
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In this paper, we first construct the controlling algebras of embedding tensors and Lie-Leibniz triples, which turn out to be a graded Lie algebra and an $L_\infty$-algebra respectively. Then weExpand

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