Separating invariants for two-dimensional orthogonal groups over finite fields

TL;DR

This paper identifies a minimal set of invariants that can distinguish orbits of m-tuples of vectors under the action of the two-dimensional orthogonal group over finite fields, advancing understanding of symmetry in finite algebraic structures.

Contribution

It introduces a minimal separating set for the algebra of invariants under the two-dimensional orthogonal group over finite fields, a novel result in invariant theory.

Findings

Explicit minimal separating set described

Enhanced understanding of invariants for orthogonal groups over finite fields

Potential applications in algebraic symmetry analysis

Abstract

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 $F_q$.