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L-infinity structures on mapping cones

Domenico Fiorenza·Marco Manetti
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Abstract

We show that the mapping cone of a morphism of differential graded Lie algebras $\chi\colon L\to M$ can be canonically endowed with an $L_\infty$-algebra structure which at the same time lifts the Lie algebra structure on $L$ and the usual differential on the mapping cone. Moreover, this structure is unique up to isomorphisms of $L_\infty$-algebras. The associated deformation functor coincides with the one introduced by the second author in arXiv:math.AG/0507287.

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Domenico Fiorenza, Marco Manetti. 2006-01-13. L-infinity structures on mapping cones. https://arxiv.org/abs/math/0601312

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