Groups acting on the ring of two 2×2 generic matrices and a coproduct decomposition of its trace ring

Formanek, Edward; Schofield, A. H.

doi:10.1090/S0002-9939-1985-0801319-4

Groups acting on the ring of two $2\times 2$ generic matrices and a coproduct decomposition of its trace ring
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by Edward Formanek and A. H. Schofield PDF

Proc. Amer. Math. Soc. 95 (1985), 179-183 Request permission

Abstract:

Two results concerning the ring $R$ generated by a pair of $2 \times 2$ generic matrices over a field $K$ are proved: (1) The trace ring of $R$ is a coproduct of commutative rings. (2) If a finite subgroup $G$ of ${\text {SL}}(2,K)$ acts homogeneously on $R$ and the characteristic of $K$ does not divide the order of $G$, then the fixed ring ${R^G}$ is a finitely generated $K$-algebra.

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Der Endlichkeitssatz der Invarianten endlicher Gruppen der Charakteristik

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L. W. Small and J. T. Stafford, Homological properties of generic matrix rings, Israel J. Math. 51 (1985), no. 1-2, 27–32. MR 804474, DOI 10.1007/BF02772956