Modular Lie algebras and the Gelfand-Kirillov conjecture

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 G_2.

20 pages

References in corpus (1)

• The Zassenhaus variety of a reductive Lie algebra in positive characteristic

Cited by in corpus (10)

• Solution of a q-difference Noether problem and the quantum Gelfand-Kirillov conjecture for gl_N
• The Zassenhaus variety of a reductive Lie algebra in positive characteristic
• The polynomiality of the Poisson center and semi-center of a Lie algebra and Dixmier's fourth problem
• Is the function field of a reductive Lie algebra purely transcendental over the field of invariants for the adjoint action?
• Non-rationality of some fibrations associated to Klein surfaces
• The Lie algebra of type G_2 is rational over its quotient by the adjoint action
• An algebra isomorphism on $U({\mathfrak{gl}}_n)$
• Gelfand-Kirillov conjecture as a first-order formula
• On Gelfand-Kirillov conjecture for some W-algebras
• Enveloping algebras of Slodowy slices and Goldie rank