A PBW theorem for inclusions of (sheaves of) Lie algebroids
type: Item
instance of: scholarly article
title: A PBW theorem for inclusions of (sheaves of) Lie algebroids
zbMATH Open document ID: 1337.53098
DOI: 10.4171/RSMUP/131-3
author: Damien Calaque
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2014-08-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1205.3214
review text: This paper is a step towards the project to construct a dictionary between Lie theory and algebraic geometry. The author first recalls the definitions and basic properties of the universal enveloping algebra, the de Rham complex and jets of a Lie algebroid. The Chen-Stienon-Xu class is then interpreted as an obstruction for extending modules to the first infinitesimal neighbourhood. A Poincaré-Birkhoff-Witt (PWB) theorem is then proved. To this end, the author uses straightforward generalizations of tools developed by Caldararu and Tu.
reviewed by: Angela Gammella-Mathieu
Mathematics Subject Classification ID: 53D17
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 16S30
zbMATH DE Number: 6329756
zbMATH Keywords: Lie algebroids
zbMATH Keywords: Atiyah class
zbMATH Keywords: PBW isomorphism
zbMATH Keywords: Poincaré-Birkhoff-Witt results
zbMATH Keywords: algebraic geometry
MaRDI profile type: Publication
arXiv ID: 1205.3214
cites work: When is the self-intersection of a subvariety a fibration?
cites work: PBW for an inclusion of Lie algebras
cites work: Hochschild cohomology and Atiyah classes
cites work: Rozansky-Witten invariants via Atiyah classes
cites work: Free Lie algebroids and the space of paths
cites work: Quantum groupoids
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description: scientific article; zbMATH DE number 6329756