### 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 | |

State | Published - Jan 1 2014 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Comptes Rendus Mathematique*,

*352*(11), 929-933. https://doi.org/10.1016/j.crma.2014.09.010

}

*Comptes Rendus Mathematique*, vol. 352, no. 11, pp. 929-933. https://doi.org/10.1016/j.crma.2014.09.010

**A Hopf algebra associated with a Lie pair.** / Chen, Zhuo; Stiénon, Mathieu; Xu, Ping.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A Hopf algebra associated with a Lie pair

AU - Chen, Zhuo

AU - Stiénon, Mathieu

AU - Xu, Ping

PY - 2014/1/1

Y1 - 2014/1/1

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

VL - 352

SP - 929

EP - 933

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 11

ER -