Roots of the affine Cremona group

Abstract

Let k[x_1,...,x_n] be the polynomial algebra in n variables and let A^n=Spec k[x_1,...,x_n]. In this note we show that the root vectors of the affine Cremona group Aut(A^n) with respect to the diagonal torus are exactly the locally nilpotent derivations x^a\times d/dx_i, where x^a is any monomial not depending on x_i. This answers a question due to Popov.

4 pages

References in corpus (1)

• Affine T-varieties of complexity one and locally nilpotent derivations

Cited by in corpus (3)

• Tori in the Cremona groups
• On homogeneous locally nilpotent derivations of trinomial algebras
• Additive group actions on affine T-varieties of complexity one in arbitrary characteristic