On separating a fixed point from zero by invariants

Jonathan Elmer* (Corresponding Author), Martin Kohls

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Assume a fixed point v∈VG can be separated from zero by a homogeneous invariant f∈k[V]G of degree prd, where p>0 is the characteristic of the ground field k and p,d are coprime. We show that then v can also be separated from zero by an invariant of degree pr, which we obtain explicitly from f. It follows that the minimal degree of a homogeneous invariant separating v from zero is a p-power.

Original languageEnglish
Pages (from-to)371-376
Number of pages6
JournalCommunications in Algebra
Volume45
Issue number1
Early online date11 Oct 2016
DOIs
Publication statusPublished - 2017

Fingerprint

Fixed point
Invariant
Zero
Coprime

Keywords

  • geometrically reductive
  • invariant theory
  • linear algebraic groups
  • prime characteristic

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On separating a fixed point from zero by invariants. / Elmer, Jonathan (Corresponding Author); Kohls, Martin.

In: Communications in Algebra, Vol. 45, No. 1, 2017, p. 371-376.

Research output: Contribution to journalArticle

Elmer, Jonathan ; Kohls, Martin. / On separating a fixed point from zero by invariants. In: Communications in Algebra. 2017 ; Vol. 45, No. 1. pp. 371-376.
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