L-infinity structures on mapping cones

Abstract

We show that the mapping cone of a morphism of differential graded Lie algebras $\chi :L\to M$ 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.

23 pages, uses xy-pic. Some major changes. Abstract modified.

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Cited by in corpus (9)

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• Higher derived brackets
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• The $L_{\infty }$-structure on symplectic cohomology
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• Lie Infinity-Algebras from Lie Rinehart Pairs
• Goto's deformation theory of geometric structures, a Lie-theoretical description
• On the L-infinity description of the Hitchin Map