Comptes Rendus
no. 17-18
Lie Algebras/Differential Geometry
Exponential map and L∞ algebra associated to a Lie pair
[Application exponentielle et algébre L∞ associée à une paire de Lie]

Présenté par : Charles-Michel Marle

Camille Laurent-Gengoux1 ; Mathieu Stiénon2 ; Ping Xu2
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, Volume 350 (2012) no. 17-18, pp. 817-821.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.08.009
Camille Laurent-Gengoux 1 ; Mathieu Stiénon 2 ; Ping Xu 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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Camille Laurent-Gengoux; Mathieu Stiénon; Ping Xu. Exponential map and $ {L}_{\infty }$ algebra associated to a Lie pair. Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 817-821. doi : 10.1016/j.crma.2012.08.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.08.009/

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[6] Camille Laurent-Gengoux; Mathieu Stiénon; Ping Xu Holomorphic Poisson manifolds and holomorphic Lie algebroids, Int. Math. Res. Not. IMRN (2008) Art. ID rnn 088, 46. MR 2439547 (2009i:53082)

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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].

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