Comptes Rendus
Differential geometry
A Hopf algebra associated with a Lie pair
Comptes Rendus. Mathématique, Volume 352 (2014) no. 11, pp. 929-933.

The quotient L/A[1] of a pair AL of Lie algebroids is a Lie algebra object in the derived category Db(A) of the category A of left U(A)-modules, the Atiyah class αL/A being its Lie bracket. In this note, we describe the universal enveloping algebra of the Lie algebra object L/A[1] and we prove that it is a Hopf algebra object in Db(A).

Le quotient L/A[1] d'une paire AL d'algébroïdes de Lie est un objet algèbre de Lie dans la catégorie dérivée Db(A) de la catégorie A des modules à gauche sur U(A). Dans cette note, nous décrivons l'algèbre enveloppante universelle de l'objet algèbre de Lie L/A[1] et nous prouvons que celle-ci constitue un objet algèbre de Hopf dans Db(A).

Published online:
DOI: 10.1016/j.crma.2014.09.010

Zhuo Chen 1; Mathieu Stiénon 2; Ping Xu 2

1 Department of Mathematics, Tsinghua University, China
2 Department of Mathematics, Penn State University, United States
     author = {Zhuo Chen and Mathieu Sti\'enon and Ping Xu},
     title = {A {Hopf} algebra associated with a {Lie} pair},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {929--933},
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     year = {2014},
     doi = {10.1016/j.crma.2014.09.010},
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Zhuo Chen; Mathieu Stiénon; Ping Xu. A Hopf algebra associated with a Lie pair. Comptes Rendus. Mathématique, Volume 352 (2014) no. 11, pp. 929-933. doi : 10.1016/j.crma.2014.09.010.

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Research partially supported by NSF grant DMS1101827, NSA grant H98230-12-1-0234, and NSFC grants 11001146 and 11471179.

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