Differential graded Lie algebras and singularities of level sets of momentum mappings
type: Item
instance of: scholarly article
title: Differential graded Lie algebras and singularities of level sets of momentum mappings
zbMATH Open document ID: 0724.58028
DOI: 10.1007/BF02098273
author: John Millson
author: William M. Goldman
published in: Communications in Mathematical Physics
publication date: 1990-01-01T00:00:00Z
review text: It is well-known that under certain conditions, the analytic germ of a level set of a momentum mapping is quadratic [see \textit{J. Arms, J. Marsden} and \textit{V. Moncrief}, Commun. Math. Phys. 78, 455-478 (1981; Zbl 0486.58008)]. In the paper under review the authors discuss some related ideas in a more algebraic context by associating to an affine Hamiltonian action a differential graded Lie algebra, which in the presence of an invariant positive complex structure is formal in the sense of \textit{P. Deligne, Ph. Griffiths, J. Morgan} and \textit{D. Sullivan} [Invent. Math. 29, 245-274 (1975; Zbl 0312.55011)].
reviewed by: Mircea Puta
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 17B70
zbMATH DE Number: 4194761
zbMATH Keywords: deformation
zbMATH Keywords: rational homotopy type
zbMATH Keywords: momentum mapping
zbMATH Keywords: affine Hamiltonian action
zbMATH Keywords: differential graded Lie algebra
MaRDI profile type: Publication
cites work: Q4174811
cites work: Symmetry and bifurcations of momentum mappings
cites work: The Yang-Mills equations over Riemann surfaces
cites work: Real homotopy theory of Kähler manifolds
cites work: The deformation theory of representations of fundamental groups of compact Kähler manifolds
cites work: The homotopy invariance of the Kuranishi space
cites work: The Lie algebra structure of tangent cohomology and deformation theory
full work available at URL: https://doi.org/10.1007/bf02098273
OpenAlex ID: W2007089813
description: scientific article; zbMATH DE number 4194761