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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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

Authors: Edward Formanek and A. H. Schofield
Journal: Proc. Amer. Math. Soc. 95 (1985), 179-183
MSC: Primary 16A38; Secondary 16A60
MathSciNet review: 801319
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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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PII: S 0002-9939(1985)0801319-4
Article copyright: © Copyright 1985 American Mathematical Society

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