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

Camille Laurent-Gengoux; Mathieu Stiénon; Ping Xu

doi:10.1016/j.crma.2012.08.009

Lie Algebras/Differential Geometry

Exponential map and

L_{\infty}

algebra associated to a Lie pair

Presented by: Charles-Michel Marle

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

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

Abstract
Résumé

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.

Received: 2012-07-13
Accepted: 2012-08-30
Published online: 2012-09-01

DOI: 10.1016/j.crma.2012.08.009

Author's affiliations:

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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     author = {Camille Laurent-Gengoux and Mathieu Sti\'enon and Ping Xu},
     title = {Exponential map and $ {L}_{\infty }$ algebra associated to a {Lie} pair},
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     pages = {817--821},
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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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Cited by Sources:

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

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