A group action on multivariate polynomials over finite fields

2017/09/13 by Reis, Lucas
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1709.04566

Abstract

Let \mathbbF_q be the finite field with q elements, where q is a power of a prime p. Recently, a particular action of the group GL₂(\mathbb F_q) on irreducible polynomials in \mathbb F_q[x] has been introduced and many questions concerning the invariant polynomials have been discussed. In this paper, we give a natural extension of this action on the polynomial ring \mathbb F_q[x₁, …, x_n] and study the algebraic properties of the invariant elements.

Related

• Invariant theory of a special group action on irreducible polynomials over finite fields
• On the existence and number of invariant polynomials
• The action of \rmGL₂(\mathbbF_q) on irreducible polynomials over \F_q
• Invariant Rational Functions, Linear Fractional Transformations and Irreducible Polynomials over Finite Fields
• Polynomial invariants of classical subgroups of GL₂: Conjugation over finite fields