The Gelfand-Kirillov conjecture for Lie algebras of dimension at most eight

DOI10.1006/jabr.1999.8192zbMath0967.17007OpenAlexW2058871845MaRDI QIDQ1569812

Alfons I. Ooms, Jacques Alev, Michel Van den Bergh

Publication date: 30 August 2000

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1999.8192

zbMATH Keywords

enveloping algebraGelfand-Kirillov conjecturealgebraic Lie algebra

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Universal enveloping algebras of Lie algebras (16S30)

Related Items

On rational isomorphisms of Lie algebras, On Dixmier's fourth problem, Solution of a \(q\)-difference Noether problem and the quantum Gelfand-Kirillov conjecture for \(\mathfrak{gl}_N\), Gelfand-Kirillov conjecture in positive characteristics, The Gelfand-Kirillov conjecture for semi-direct products of Lie algebras, The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite \(W\)-algebras, The maximal abelian dimension of a Lie algebra, Rentschler's property and Milovanov's conjecture, The Frobenius semiradical of a Lie algebra., Some open problems in the context of skew \textit{PBW} extensions and semi-graded rings, SUR LES INVARIANTS DE B_λSOUS L'ACTION DE SOUS-GROUPES FINIS D'AUTOMORPHISMES: CONJECTURE DE GELFAND-KIRILLOV ET HOMOLOGIE DE HOCHSCHILD, The polynomiality of the Poisson center and semi-center of a Lie algebra and Dixmier's fourth problem, Modular Lie algebras and the Gelfand-Kirillov conjecture, Computing invariants and semi-invariants by means of Frobenius Lie algebras, Enveloping skewfields of the nilpotent positive part and the Borel subsuperalgebra of \large𝔬𝔰𝔭(1,2𝔫)

Cites Work

• Unnamed Item
• Unnamed Item
• Ideaux primitifs des algèbres enveloppantes
• Primideale in Einhüllenden auflösbarer Lie-Algebren (Beschreibung durch Bahnenräume)
• Sur les corps liés aux algèbres enveloppantes des algèbres de Lie
• The structure of the Lie field connected with a split semisimple Lie algebra
• Réduction de produits semi-directs et conjecture de Gel'fand et Kirillov
• Sur Les Représentations Unitaires Des Groupes De Lie Nilpotents. III
• Low-dimensional real Lie algebras
• Proof of the Gelfand-Kirillov Conjecture for Solvable Lie Algebras
• Sur le semi-centre du corps enveloppant d'une algèbre de Lie
• Representations of Solvable Lie Algebras and the Gelfand-Kirillov Conjecture
• On Lie Algebras with Primitive Envelopes, Supplements
• A Generalization of the Gelfand-Kirillov Conjecture
• A class of counterexamples to the Gel’fand-Kirillov conjecture