L∞ structures on mapping cones

Fiorenza, Domenico; Manetti, Marco

doi:10.2140/ant.2007.1.301

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

Domenico Fiorenza and Marco Manetti

Vol. 1 (2007), No. 3, 301–330

DOI: 10.2140/ant.2007.1.301

Abstract

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

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/

Vol. 1, No. 3, 2007