This article is cited in 3 papers

Action of biregular automorphisms of the affine plane on pairs of matrices

I. V. Artamkin


Abstract: A study is made of the natural action of the group of biregular automorphisms of the affine plane on pairs of square matrices and pairs of symmetric square matrices. It is proved that in the open set of pairs $(A,B)$ such that $A$ is semisimple and $A$ and $B$ have no common invariant subspaces, the commutator $[A,B]=AB-BA$ is the unique invariant in both cases.
Bibliography: 3 titles.

UDC: 512.7

MSC: Primary 20B27, 14L17; Secondary 14L15

Received: 16.02.1987

 English version: Mathematics of the USSR-Izvestiya, 1989, 33:2, 433–439

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