Cyclic homology of enveloping algebras
type: Item
instance of: scholarly article
title: Cyclic homology of enveloping algebras
zbMATH Open document ID: 0653.17007
DOI: 10.1007/BF01389366
author: Christian Kassel
published in: Inventiones Mathematicae
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143538
review text: L'A. met en relation des invariants algébriques d'une algèbre de Lie \({\mathfrak g}\), à savoir l'homologie de Hochschild et l'homologie cyclique de son algèbre enveloppante (\U({\mathfrak g})\), avec les invariants géométriques de la structure de Poisson sur le dual \({\mathfrak g}\) * (structure de Kirillov). \par Le complexe de de Rham d'une variété de Poisson peut être muni d'une différentielle \(\delta\) de degré \(-1\) (ce résultat est dû à Lichnerowicz et Brylinski): l'homologie obtenue est alors l'homologie de Hochschild de (\U({\mathfrak g}).\) \par D'autre part cette différentielle \(\delta\) commute à la différentielle de de Rham et l'homologie totale du bicomplexe obtenue est identique à l'homologie cyclique de (\U({\mathfrak g})\). L'A. utilise ensuite son théorème pour analyser la suite spectrale de Connes convergeant vers l'homologie cyclique: Ainsi pour les algèbres enveloppantes des algèbres de Lie semisimples, cette suite spectrale ne dégénère jamais au terme \(E^2\).
reviewed by: Claude Roger
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 55T99
zbMATH DE Number: 4065224
zbMATH Keywords: Hochschild homology
zbMATH Keywords: enveloping algebra
zbMATH Keywords: Poisson structure
zbMATH Keywords: Connes spectral sequence
zbMATH Keywords: cyclic homology
zbMATH Keywords: semisimple Lie algebras
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4065224