Separating invariants over finite fields

Gregor Kemper; Artem Lopatin; Fabian Reimers

doi:10.1016/j.jpaa.2021.106904

Separating invariants over finite fields

Gregor Kemper
, Artem Lopatin
, Fabian Reimers

Chair of Algorithmic Algebra

University of Campinas
Technical University of Munich

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

14 Scopus citations

Abstract

We determine the minimal number of separating invariants for the invariant ring of a matrix group G≤GL_n(F_q) over the finite field F_q. We show that this minimal number can be obtained with invariants of degree at most |G|n(q−1). In the non-modular case this construction can be improved to give invariants of degree at most n(q−1). As examples we study separating invariants over the field F₂ for two important representations of the symmetric group.

Original language	English
Article number	106904
Journal	Journal of Pure and Applied Algebra
Volume	226
Issue number	4
DOIs	https://doi.org/10.1016/j.jpaa.2021.106904
State	Published - Apr 2022

Keywords

Generators
Invariant theory
Multisymmetric polynomials
Positive characteristic
Relations
Separating invariants
Symmetric group

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10.1016/j.jpaa.2021.106904

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title = "Separating invariants over finite fields",

abstract = "We determine the minimal number of separating invariants for the invariant ring of a matrix group G≤GLn(Fq) over the finite field Fq. We show that this minimal number can be obtained with invariants of degree at most |G|n(q−1). In the non-modular case this construction can be improved to give invariants of degree at most n(q−1). As examples we study separating invariants over the field F2 for two important representations of the symmetric group.",

keywords = "Generators, Invariant theory, Multisymmetric polynomials, Positive characteristic, Relations, Separating invariants, Symmetric group",

author = "Gregor Kemper and Artem Lopatin and Fabian Reimers",

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AU - Lopatin, Artem

AU - Reimers, Fabian

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AB - We determine the minimal number of separating invariants for the invariant ring of a matrix group G≤GLn(Fq) over the finite field Fq. We show that this minimal number can be obtained with invariants of degree at most |G|n(q−1). In the non-modular case this construction can be improved to give invariants of degree at most n(q−1). As examples we study separating invariants over the field F2 for two important representations of the symmetric group.

KW - Generators

KW - Invariant theory

KW - Multisymmetric polynomials

KW - Positive characteristic

KW - Relations

KW - Separating invariants

KW - Symmetric group

UR - https://www.scopus.com/pages/publications/85114389838

U2 - 10.1016/j.jpaa.2021.106904

DO - 10.1016/j.jpaa.2021.106904

M3 - Article

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SN - 0022-4049

VL - 226

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 4

M1 - 106904

ER -

Separating invariants over finite fields

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Keywords

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