Exponential map and L ∞ algebra associated to a Lie pair

Camille Laurent-Gengoux; Mathieu Stiénon; Ping Xu

doi:10.1016/j.crma.2012.08.009

Exponential map and L _∞ algebra associated to a Lie pair

Camille Laurent-Gengoux
, Mathieu Stiénon
, Ping Xu

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	817-821
Number of pages	5
Journal	Comptes Rendus Mathematique
Volume	350
Issue number	17-18
DOIs	https://doi.org/10.1016/j.crma.2012.08.009
State	Published - Sep 2012

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.crma.2012.08.009

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title = "Exponential map and L ∞ algebra associated to a Lie pair",

abstract = "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.",

author = "Camille Laurent-Gengoux and Mathieu Sti{\'e}non and Ping Xu",

note = "Funding Information: Research partially supported by the National Science Foundation [DMS-1101827] and the National Security Agency [H98230-12-1-0234]. E-mail addresses: [email protected] (C. Laurent-Gengoux), [email protected] (M. Sti{\'e}non), [email protected] (P. Xu).",

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AU - Laurent-Gengoux, Camille

AU - Stiénon, Mathieu

AU - Xu, Ping

N1 - Funding Information: Research partially supported by the National Science Foundation [DMS-1101827] and the National Security Agency [H98230-12-1-0234]. E-mail addresses: [email protected] (C. Laurent-Gengoux), [email protected] (M. Stiénon), [email protected] (P. Xu).

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N2 - 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.

AB - 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.

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UR - https://www.scopus.com/pages/publications/84868157270#tab=citedBy

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ER -

Exponential map and L _∞ algebra associated to a Lie pair

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