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Article Dans Une Revue Moscow Mathematical Journal Année : 2016

Pre-Lie deformation theory

Vladimir Dotsenko
Sergey Shadrin
  • Fonction : Auteur
Bruno Vallette

Résumé

In this paper, we develop the deformation theory controlled by pre-Lie algebras; the main tool is a new integration theory for pre-Lie algebras. The main field of application lies in homotopy algebra structures over a Koszul operad; in this case, we provide a homotopical description of the associated Deligne groupoid. This permits us to give a conceptual proof, with complete formulae, of the Homotopy Transfer Theorem by means of gauge action. We provide a clear explanation of this latter ubiquitous result: there are two gauge elements whose action on the original structure restrict its inputs and respectively its output to the homotopy equivalent space. This implies that a homotopy algebra structure transfers uniformly to a trivial structure on its underlying homology if and only if it is gauge trivial; this is the ultimate generalization of the d-dbar lemma.

Dates et versions

hal-01142685 , version 1 (15-04-2015)

Identifiants

Citer

Vladimir Dotsenko, Sergey Shadrin, Bruno Vallette. Pre-Lie deformation theory. Moscow Mathematical Journal, 2016, July-September 2016, 16 (3), pp.505-543. ⟨10.17323/1609-4514-2016-16-3-505-543⟩. ⟨hal-01142685⟩
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