The differential invariants of SL₂(\mathbbF₃) acting on trace-free matrices over \mathbbF₃

2025/12/12 by Elmer, Jonathan, Meyer, Anja
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Commutative Algebra and Its Applications

paper · doi:10.48550/arxiv.2512.11702

Abstract

Let M denote the vector space of 2 × 2 matrices with coefficients in \mathbbF₃ and trace zero. Let G = SL₂(\mathbbF₃). Then G acts on M via conjugation. Let R =(S(M^*) ⊗ Λ(M^*)) be the algebra of differential forms on M. We compute a minimal generating set for R^G as a commutative-graded algebra. In doing so we utilise the theory of Cohen-Macaulay modules and results in the theory of covariants.

Citations

• Cohen-Macaulay modules of covariants for cyclic p-groups
• Cohen-Macaulay Rings, Invariant Theory, and the Generic Perfection of Determinantal Loci

Related

• Classical invariant theory for free metabelian Lie algebras
• Differential identities of matrix algebras
• Computing with matrix invariants
• On graded polynomial identities of sl₂(F) over a finite field
• Algebraic and analytic properties of invariant differential operators on a homogeneous space of complexity 1