TY - JOUR

T1 - On the finite generation of additive group invariants in positive characteristic

AU - Dufresne, Emilie

AU - Maurischat, Andreas

PY - 2010/10/1

Y1 - 2010/10/1

N2 - Roberts, Freudenburg, and Daigle and Freudenburg have given the smallest counterexamples to Hilbert's fourteenth problem as rings of invariants of algebraic groups. Each is of an action of the additive group on a finite dimensional vector space over a field of characteristic zero, and thus, each is the kernel of a locally nilpotent derivation. In positive characteristic, additive group actions correspond to locally finite iterative higher derivations. We set up characteristic-free analogs of the three examples, and show that, contrary to characteristic zero, in every positive characteristic, the invariants are finitely generated.

AB - Roberts, Freudenburg, and Daigle and Freudenburg have given the smallest counterexamples to Hilbert's fourteenth problem as rings of invariants of algebraic groups. Each is of an action of the additive group on a finite dimensional vector space over a field of characteristic zero, and thus, each is the kernel of a locally nilpotent derivation. In positive characteristic, additive group actions correspond to locally finite iterative higher derivations. We set up characteristic-free analogs of the three examples, and show that, contrary to characteristic zero, in every positive characteristic, the invariants are finitely generated.

KW - Hilbert's fourteenth problem

KW - Locally finite iterative higher derivations

UR - http://www.scopus.com/inward/record.url?scp=77955923167&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2010.05.023

DO - 10.1016/j.jalgebra.2010.05.023

M3 - Article

AN - SCOPUS:77955923167

SN - 0021-8693

VL - 324

SP - 1952

EP - 1963

JO - Journal of Algebra

JF - Journal of Algebra

IS - 8

ER -