#### Vol. 1, No. 3, 2007

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L$\mskip1mu _{\infty}$ structures on mapping cones

### Domenico Fiorenza and Marco Manetti

Vol. 1 (2007), No. 3, 301–330
##### 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.

##### Keywords
differential graded Lie algebra, symmetric coalgebra, $L_{\infty}$-algebra, functor of Artin ring
Primary: 17B70
Secondary: 13D10