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, 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, $L_{\infty}$-algebra, functor of Artin ring
Mathematical Subject Classification 2000
Primary: 17B70
Secondary: 13D10
Milestones
Received: 3 April 2007
Revised: 7 August 2007
Accepted: 5 September 2007
Published: 1 August 2007
Authors
Domenico Fiorenza
Dipartimento di Matematica “Guido Castelnuovo”
Università di Roma “La Sapienza”
Piazzale Aldo Moro 5
I-00185 Roma
Italy
http://www.mat.uniroma1.it/\~{}fiorenza/
Marco Manetti
Dipartimento di Matematica “Guido Castelnuovo”
Università di Roma “La Sapienza”
Piazzale Aldo Moro 5
I-00185 Roma
Italy
http://www.mat.uniroma1.it/people/manetti/