Dave Anderson, Mathieu Florence and Zinovy Reichstein: The Lie algebra of type G_2 is rational over its quotient by the adjoint action

dave@impa.br, mathieu.florence@gmail.com and reichst@math.ubc.ca

Submission: 2013, Aug 27

Let G be a split simple group of type G_2 over a field k, and let g be its Lie algebra. We show that the function field k(g) is generated by algebraically independent elements over the field of adjoint invariants k(g)^G.

2010 Mathematics Subject Classification: 14E08, 17B45, 14L30

Keywords and Phrases: Algebraic group, Lie algebra, G_2, rationality problem, Gelfand-Kirillov conjecture

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