Related papers: Separating invariants over finite fields

We described a minimal separating set for the algebra of $O(F_q)$-invariant polynomial functions of $m$-tuples of two-dimensional vectors over a finite field $F_q$.

Given an algebra $F[H]^G$ of polynomial invariants of an action of the group $G$ over the vector space $H$, a subset $S$ of $F[H]^G$ is called separating if $S$ separates all orbits that can be separated by $F[H]^G$. A minimal separating…

A minimal separating set is found for the algebra of matrix invariants of several 2x2 matrices over an infinite field of arbitrary characteristic

If V is a representation of a linear algebraic group G, a set S of G-invariant regular functions on V is called separating if the following holds: If two elements v,v' from V can be separated by an invariant function, then there is an f…

We describe separating G_2-invariants of several copies of the algebra of octonions over an algebraically closed field of characteristic two. We also obtain a minimal separating and a minimal generating set for G_2-invariants of several…

It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating…

Let ${\mathbb{F}_{q}}$ be the finite field of order $q$. Let $G$ be one of the three groups ${\rm GL}(n, \mathbb{F}_q)$, ${\rm SL}(n, \mathbb{F}_q)$ or ${\rm U}(n, \mathbb{F}_q)$ and let $W$ be the standard $n$-dimensional representation of…

Suppose that G is a linearly reductive group. We study the minimal free resolution of the invariant ring. If G is a finite linearly reductive group, then the ring of invariants is generated in degree at most |G|, the group order. We prove…

This article studies separating invariants for the ring of multisymmetric polynomials in $m$ sets of $n$ variables over an arbitrary field $\mathbb{K}$. We prove that in order to obtain separating sets it is enough to consider polynomials…

Let $G$ be a linear algebraic group acting linearly on a vector space $V$, and let $k[V]^G$ be the corresponding algebra of invariant polynomial functions. A separating set $S \subseteq k[V]^G$ is a set of polynomials with the property that…

The study of separating invariants is a recent trend in invariant theory. For a finite group acting linearly on a vector space, a separating set is a set of invariants whose elements separate the orbits of G. In some ways, separating sets…

The algebra of ${\rm GL}_n$-invariants of $m$-tuples of $n\times n$ matrices with respect to the action by simultaneous conjugation is a classical topic in case of infinite base field. On the other hand, in case of a finite field generators…

We find a formula for the number of permutation polynomials of degree q-2 over a finite field Fq, which has q elements, in terms of the permanent of a matrix. We write down an expression for the number of permutation polynomials of degree…

We fix a field $\kk$ of characteristic $p$. For a finite group $G$ denote by $\delta(G)$ and $\sigma(G)$ respectively the minimal number $d$, such that for any finite dimensional representation $V$ of $G$ over $\kk$ and any $v\in…

Consider a Noetherian domain $R$ and a finite group $G \subseteq Gl_n(R)$. We prove that if the ring of invariants $R[x_1, \ldots, x_n]^G$ is a Cohen-Macaulay ring, then it is generated as an $R$-algebra by elements of degree at most…

We determine the rings of invariants in the symmetric algebra on the dual of a vector space V over the field of two elements, for the group G of orthogonal transformations preserving a non-singular quadratic form on V. The invariant ring is…

In this paper we study the algebra of graph invariants, focusing mainly on the invariants of simple graphs. All other invariants, such as sorted eigenvalues, degree sequences and canonical permutations, belong to this algebra. In fact,…

For modular indecomposable representations of a cyclic group $G$ of prime order $p$ we propose a list of polynomial invariants of degree $\leq 3$ that, together with a simple invariant of degree $p$, separate generic orbits and generate the…

The set $S(n)$ of all elementary symmetric polynomials in $n$ variables is a minimal generating set for the algebra of symmetric polynomials in $n$ variables, but over a finite field ${\mathbb F}_q$ the set $S(n)$ is not a minimal…

We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.