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Comptes Rendus Mathématique
Volume 352, n° 11
pages 929-933 (novembre 2014)
Doi : 10.1016/j.crma.2014.09.010
Received : 6 August 2013 ;  accepted : 16 September 2014
A Hopf algebra associated with a Lie pair
Une algèbre de Hopf associée à une paire de Lie

Zhuo Chen a , Mathieu Stiénon b , Ping Xu b
a Department of Mathematics, Tsinghua University, China 
b Department of Mathematics, Penn State University, United States 


The quotient   of a pair   of Lie algebroids is a Lie algebra object in the derived category   of the category   of left  -modules, the Atiyah class   being its Lie bracket. In this note, we describe the universal enveloping algebra of the Lie algebra object   and we prove that it is a Hopf algebra object in  .

The full text of this article is available in PDF format.

Le quotient   d'une paire   d'algébroïdes de Lie est un objet algèbre de Lie dans la catégorie dérivée   de la catégorie   des modules à gauche sur  . Dans cette note, nous décrivons l'algèbre enveloppante universelle de l'objet algèbre de Lie   et nous prouvons que celle-ci constitue un objet algèbre de Hopf dans  .

The full text of this article is available in PDF format.

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

1  An  -shuffle is a permutation σ of the set   such that   and  .

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