Abstract

We show that the mapping cone of a morphism of differential graded Lie algebras, χ: L → M, can be canonically endowed with an L_∞-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_∞-algebras.

Keywords

differential graded Lie algebra, symmetric coalgebra, L_∞-algebra, functor of Artin ring

Mathematical Subject Classification

Primary: 17B70

Secondary: 13D10

Authors