The BGG complex on projective space
type: Item
instance of: scholarly article
title: The BGG complex on projective space
zbMATH Open document ID: 1251.58007
DOI: 10.3842/SIGMA.2011.060
author: Rod Gover
author: M. Eastwood
published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
publication date: 2012-06-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/1106.4623
review text: The article is related to differential calculus on real or complex projective space invariant with respect to projective transformations forming a semisimple Lie group. The Bernstein-Gelfand-Gelfand (BGG) complexes on \(\mathbb{RP}_n\) or \(\mathbb{CP}_n\) are complexes of vector bundles and differential operators between them the generalizing de Rham complex on \(\mathbb{RP}_n\) and the holomorphic de Rham complex on \(\mathbb{CP}_n\) respectively. Here, employing the projective invariance, the authors derive explicit formulae for the operators in the projective BGG complex on \(\mathbb{RP}_n\) in terms of the usual round metric on the sphere \(S^n\) as its double cover.
Mathematics Subject Classification ID: 58J10
Mathematics Subject Classification ID: 53A20
Mathematics Subject Classification ID: 58J70
Mathematics Subject Classification ID: 17B56
zbMATH DE Number: 6050679
zbMATH Keywords: differential complex
zbMATH Keywords: projective space
zbMATH Keywords: Lie algebra cohomology
zbMATH Keywords: parabolic geometry
zbMATH Keywords: Bernstein-Gelfand-Gelfand (BGG) complexes
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
arXiv ID: 1106.4623
OpenAlex ID: W2112330306
description: scientific article; zbMATH DE number 6050679