L-infinity structures on mapping cones

Details L-infinity structures on mapping cones L-infinity structures on mapping cones

2006-01-13

arxiv.org/abs/math/0601312v3

Algebra & Number Theory, Vol. 1, No. 3 (2007), 301-330.

Mathematics

Quantum Algebra

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

Scientific paper

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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