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July 3, 2026Journal of Algebra and Its Applications0 citationsOpen Access

Some Four-Dimensional Orthogonal Invariants

SRShan RenRZRunxuan Zhang

Key Points

  • This research aims to compute the invariant ring for a four-dimensional orthogonal group over a prime field.
  • Examine the action of an odd prime-dimensional orthogonal group on the standard representation and dual space.
  • Explicitly exhibit a minimal generating set for the invariant ring.
  • Successfully compute the invariant ring derived from the orthogonal group.
  • Demonstrate applications of the computed invariants in the covariant theory of finite groups.

Abstract

Let Formula: see text be an odd prime and Formula: see text be the prime field of order Formula: see text. Consider a Formula: see text-dimensional orthogonal group Formula: see text over Formula: see text acting on the standard representation Formula: see text and the dual space Formula: see text. We compute the invariant ring Formula: see text via explicitly exhibiting a minimal generating set. Our method provides an application of the Formula: see text-invariants appearing in the covariant theory of finite groups.

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Cite This Study

Ren et al. (2026) studied this question.

synapsesocial.com/papers/6a4750705c29257aa25782afhttps://doi.org/10.1142/s0219498828500041
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Also Consider

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  5. 5The Spherical Realization of the Triad: Dimensional Selection by the Isolated Antipodal Fixed-Point Pair, and the Two 4π's2026