Dans cette note, nous dévoilons des structures algébriques, riches en homotopies, engendrées par les classes dʼAtiyah relatives à une paire de Lie dʼalgébroïdes. En particulier, nous prouvons que le quotient 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 of algebroids. In particular, we prove that the quotient 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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@article{CRMATH_2012__350_17-18_817_0, author = {Laurent-Gengoux, Camille and Sti\'enon, Mathieu and Xu, Ping}, title = {Exponential map and $ {L}_{\infty }$ algebra associated to a {Lie} pair}, journal = {Comptes Rendus. Math\'ematique}, pages = {817--821}, publisher = {Elsevier}, volume = {350}, number = {17-18}, year = {2012}, doi = {10.1016/j.crma.2012.08.009}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2012.08.009/} }
TY - JOUR AU - Laurent-Gengoux, Camille AU - Stiénon, Mathieu AU - Xu, Ping TI - Exponential map and $ {L}_{\infty }$ algebra associated to a Lie pair JO - Comptes Rendus. Mathématique PY - 2012 SP - 817 EP - 821 VL - 350 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.08.009/ DO - 10.1016/j.crma.2012.08.009 LA - en ID - CRMATH_2012__350_17-18_817_0 ER -
%0 Journal Article %A Laurent-Gengoux, Camille %A Stiénon, Mathieu %A Xu, Ping %T Exponential map and $ {L}_{\infty }$ algebra associated to a Lie pair %J Comptes Rendus. Mathématique %D 2012 %P 817-821 %V 350 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.08.009/ %R 10.1016/j.crma.2012.08.009 %G en %F CRMATH_2012__350_17-18_817_0
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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☆ Research partially supported by the National Science Foundation [DMS-1101827] and the National Security Agency [H98230-12-1-0234].