Nonexistence of negative weight derivations on graded Artin algebras: A conjecture of Halperin
type: Item
instance of: scholarly article
title: Nonexistence of negative weight derivations on graded Artin algebras: A conjecture of Halperin
zbMATH Open document ID: 0952.13006
author: Hao Chen
published in: Journal of Algebra
publication date: 1999-10-10T00:00:00Z
review text: S.~Halperin conjectured that if \(F\to E\to B\) is a fibration with simply connected base \(B\), and if the rational cohomology algebra of \(F\) is an Artin algebra of the form \(Q[x_{0},\ldots,x_{n}]/(f_{0},\ldots,f_{n})\), then the Serre spectral sequence for the fibration collapses. The conjecture can be stated algebraically in terms of the nonexistence of negative weight derivations on rings such as the one described above. Here, the conjecture is proven for \(n=2\).
Mathematics Subject Classification ID: 13E10
Mathematics Subject Classification ID: 14D06
Mathematics Subject Classification ID: 13N15
zbMATH DE Number: 1309245
zbMATH Keywords: fibration
zbMATH Keywords: Serre spectral sequence
zbMATH Keywords: negative weight derivation
reviewed by: William H. Gustafson
MaRDI profile type: Publication
full work available at URL: jabr.1998.7750
OpenAlex ID: W2034243466
cites work: Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi
cites work: Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts
cites work: Nonexistence of negative weight derivation of moduli algebras of weighted homogeneous singularities
cites work: On negative weight derivations of the moduli algebras of weighted homogeneous hypersurface singularities
cites work: Q4200481
cites work: Rational universal fibrations and flag manifolds
cites work: On Hartshorne's conjecture
cites work: Q3888184
cites work: Rational homotopy of Serre fibrations
cites work: Derivations of negative weight and non-smoothability of certain singularities
cites work: Q3317211
cites work: A cohomological characterization of \({\mathbb{P}}^ n\)
cites work: Solvability of Lie Algebras Arising from Isolated Singularities and Nonisolatedness of Singularities Defined by sℓ(2, C) Invariant Polynomials
DOI: 10.1006/JABR.1998.7750
Wikidata QID: Q123251236
description: scientific article; zbMATH DE number 1309245