Exponential map and $ {L}_{\infty }$ algebra associated to a Lie pair

Laurent-Gengoux, Camille; Stiénon, Mathieu; Xu, Ping

doi:10.1016/j.crma.2012.08.009

Lie Algebras/Differential Geometry

Exponential map and

L_{\infty}

algebra associated to a Lie pair
[Application exponentielle et algébre

L_{\infty}

associée à une paire de Lie]

Présenté par : Charles-Michel Marle

Laurent-Gengoux, Camille ¹ ; Stiénon, Mathieu ² ; Xu, Ping ²

¹ Département de mathématiques, université de Lorraine, île du Saulcy, 57000 Metz, France
² Department of Mathematics, Penn State University, University Park, PA 16802, USA

Comptes Rendus. Mathématique, Tome 350 (2012) no. 17-18, pp. 817-821.

Résumé
Abstract

Dans cette note, nous dévoilons des structures algébriques, riches en homotopies, engendrées par les classes dʼAtiyah relatives à une paire de Lie $(L, A)$ dʼalgébroïdes. En particulier, nous prouvons que le quotient $L / A$ dʼune telle paire admet une structure essentiellement canonique de module à homotopie près sur lʼalgébroïde de Lie A que nous appelons module de Kapranov.

In this Note, we unveil homotopy-rich algebraic structures generated by the Atiyah classes relative to a Lie pair $(L, A)$ of algebroids. In particular, we prove that the quotient $L / A$ of such a pair admits an essentially canonical homotopy module structure over the Lie algebroid A, which we call Kapranov module.

Reçu le : 2012-07-13
Accepté le : 2012-08-30
Publié le : 2012-09-01

DOI : 10.1016/j.crma.2012.08.009

Affiliations des auteurs :

Laurent-Gengoux, Camille ¹ ; Stiénon, Mathieu ² ; Xu, Ping ²

¹ Département de mathématiques, université de Lorraine, île du Saulcy, 57000 Metz, France
² Department of Mathematics, Penn State University, University Park, PA 16802, USA

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     title = {Exponential map and $ {L}_{\infty }$ algebra associated to a {Lie} pair},
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Laurent-Gengoux, Camille; Stiénon, Mathieu; Xu, Ping. Exponential map and $ {L}_{\infty }$ algebra associated to a Lie pair. Comptes Rendus. Mathématique, Tome 350 (2012) no. 17-18, pp. 817-821. doi : 10.1016/j.crma.2012.08.009. http://www.numdam.org/articles/10.1016/j.crma.2012.08.009/

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Cité par Sources :

^☆ Research partially supported by the National Science Foundation [DMS-1101827] and the National Security Agency [H98230-12-1-0234].