The differential invariants of SL2(𝔽3) acting on trace-free matrices over 𝔽3

Let M denote the vector space of 2×2 matrices with coefficients in 𝔽3 and trace zero. Let 𝐺=SL2⁢(𝔽3). 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 𝑅𝐺 as a commutative-graded algebra. In doing so we utilize the theory of Cohen-Macaulay modules and results in the theory of covariants.

Let M denote the vector space of 2 × 2 matrices with coefficients in F_3 and trace zero. Let G = SL_2(F_3). 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.

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