Artem Lopatin

collaborators

3 papers

math.AC2024

Separating symmetric polynomials over finite fields

Artem Lopatin, Pedro Antonio Muniz Martins, Lael Viana Lima

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 fie…

math.AC2023

Separating invariants for two-dimensional orthogonal groups over finite fields

Artem Lopatin, Pedro Antonio Muniz Martins

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 $F_{q}$ .

math.RA2023

On m-tuples of nilpotent 2x2 matrices over an arbitrary field

Artem Lopatin

The algebra of $GL_{n}$ -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 fi…