Modular Lie algebras and the Gelfand–Kirillov conjecture

2009/07/15 by Alexander Premet
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Algebraically closed field #Conjecture #Field (mathematics) #Lie algebra #Mathematics #Modular design #Pure mathematics #Simple (philosophy) #Type (biology) #Zero (linguistics) #math.RA #math.RT #msc:17B20 #msc:17B35 #msc:17B50

paper · pdf · doi:10.1007/s00222-010-0249-8

20 pages

arxiv created 2009/07/15 · openalex publication_date 2010/04/20 · arxiv updated 2015/05/13 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05

Abstract

Let g be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero. We show that if the Gelfand-Kirillov conjecture holds for g, then g has type A_n, C_n or G₂.

Citations

• Ample Subvarieties of Algebraic Varieties
• Graduate Texts in Mathematics
• Basic Algebraic Geometry 2