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
Laurent-Gengoux, Camille1 ; Stiénon, Mathieu2 ; Xu, Ping2
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

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.08.009

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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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

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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].