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}
}
• Published 2020
• Physics, Mathematics
• arXiv: Mathematical Physics
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
Differential Graded Lie Algebras and Leibniz Algebra Cohomology
In this note, we interpret Leibniz algebras as differential graded Lie algebras. Namely, we consider two functors from the category of Leibniz algebras to that of differential graded Lie algebras andExpand
The Controlling $$L_\infty$$-Algebra, Cohomology and Homotopy of Embedding Tensors and Lie–Leibniz Triples
• Mathematics, Physics
• 2020
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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