On separating a fixed point from zero by invariants

Jonathan Elmer; Martin Kohls

doi:10.1080/00927872.2016.1175465

On separating a fixed point from zero by invariants

Jonathan Elmer^* (Corresponding Author), Martin Kohls

^*Corresponding author for this work

Mathematical Science

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Abstract

Assume a fixed point v∈V^G can be separated from zero by a homogeneous invariant f∈k[V]^G of degree p^rd, 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 p^r, 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 language	English
Pages (from-to)	371-376
Number of pages	6
Journal	Communications in Algebra
Volume	45
Issue number	1
Early online date	11 Oct 2016
DOIs	https://doi.org/10.1080/00927872.2016.1175465
Publication status	Published - 2017

Keywords

geometrically reductive
invariant theory
linear algebraic groups
prime characteristic

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AB - 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.

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KW - invariant theory

KW - linear algebraic groups

KW - prime characteristic

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On separating a fixed point from zero by invariants

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Keywords

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