On the finite generation of additive group invariants in positive characteristic

Emilie Dufresne; Andreas Maurischat

doi:10.1016/j.jalgebra.2010.05.023

On the finite generation of additive group invariants in positive characteristic

Emilie Dufresne^*, Andreas Maurischat

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1952-1963
Number of pages	12
Journal	Journal of Algebra
Volume	324
Issue number	8
DOIs	https://doi.org/10.1016/j.jalgebra.2010.05.023
Publication status	Published - 1 Oct 2010

Keywords

Hilbert's fourteenth problem
Locally finite iterative higher derivations

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10.1016/j.jalgebra.2010.05.023

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On the finite generation of additive group invariants in positive characteristic

Abstract

Keywords

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