A Hopf algebra associated with a Lie pair

Zhuo Chen; Mathieu Stiénon; Ping Xu

doi:10.1016/j.crma.2014.09.010

A Hopf algebra associated with a Lie pair

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Abstract

The quotient L/A[-1] of a pair A {right arrow, hooked} L of Lie algebroids is a Lie algebra object in the derived category D^b(A) of the category A of left U(A)-modules, the Atiyah class α_L/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 D^b(A).

Original language	English (US)
Pages (from-to)	929-933
Number of pages	5
Journal	Comptes Rendus Mathematique
Volume	352
Issue number	11
DOIs	https://doi.org/10.1016/j.crma.2014.09.010
State	Published - 2014

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.crma.2014.09.010

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abstract = "The quotient L/A[-1] of a pair A \{right arrow, hooked\} L 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).",

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year = "2014",

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A Hopf algebra associated with a Lie pair

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