### Abstract

Assume a fixed point v∈V^{G} can be separated from zero by a homogeneous invariant f∈k[V]^{G} of degree p^{r}d, 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 |
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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 | |

Publication status | Published - 2017 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Communications in Algebra*,

*45*(1), 371-376. https://doi.org/10.1080/00927872.2016.1175465

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

Research output: Contribution to journal › Article

*Communications in Algebra*, vol. 45, no. 1, pp. 371-376. https://doi.org/10.1080/00927872.2016.1175465

}

TY - JOUR

T1 - On separating a fixed point from zero by invariants

AU - Elmer, Jonathan

AU - Kohls, Martin

PY - 2017

Y1 - 2017

N2 - 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.

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.

KW - geometrically reductive

KW - invariant theory

KW - linear algebraic groups

KW - prime characteristic

UR - http://www.scopus.com/inward/record.url?scp=84990990290&partnerID=8YFLogxK

U2 - 10.1080/00927872.2016.1175465

DO - 10.1080/00927872.2016.1175465

M3 - Article

AN - SCOPUS:84990990290

VL - 45

SP - 371

EP - 376

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 1

ER -