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

Zhuo Chen, Mathieu Stiénon, Ping Xu

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

4 Scopus citations

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

Mathematics(all)

Access to Document

10.1016/j.crma.2014.09.010

Cite this

@article{7523ab96bd524904a6c903b545257792,

title = "A Hopf algebra associated with a Lie pair",

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).",

author = "Zhuo Chen and Mathieu Sti{\'e}non and Ping Xu",

note = "Publisher Copyright: {\textcopyright} 2014 Acad{\'e}mie des sciences.",

year = "2014",

doi = "10.1016/j.crma.2014.09.010",

language = "English (US)",

volume = "352",

pages = "929--933",

journal = "Comptes Rendus Mathematique",

issn = "1631-073X",

publisher = "Elsevier Masson",

number = "11",

}

TY - JOUR

T1 - A Hopf algebra associated with a Lie pair

AU - Chen, Zhuo

AU - Stiénon, Mathieu

AU - Xu, Ping

PY - 2014

Y1 - 2014

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=84927665867&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84927665867&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2014.09.010

DO - 10.1016/j.crma.2014.09.010

M3 - Article

AN - SCOPUS:84927665867

SN - 1631-073X

VL - 352

SP - 929

EP - 933

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 11

ER -

A Hopf algebra associated with a Lie pair

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this