Geodesic
Action of biregular automorphisms of the affine plane on pairs of matrices
Izvestiya. Mathematics , Tome 33 (1989) no. 2, pp. 433-439.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_1989_33_2_a12,
     author = {I. V. Artamkin},
     title = {Action of biregular automorphisms of the affine plane on pairs of matrices},
     journal = {Izvestiya. Mathematics },
     pages = {433--439},
     publisher = {mathdoc},
     volume = {33},
     number = {2},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1989_33_2_a12/}
}
TY  - JOUR
AU  - I. V. Artamkin
TI  - Action of biregular automorphisms of the affine plane on pairs of matrices
JO  - Izvestiya. Mathematics 
PY  - 1989
SP  - 433
EP  - 439
VL  - 33
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1989_33_2_a12/
LA  - en
ID  - IM2_1989_33_2_a12
ER  - 
%0 Journal Article
%A I. V. Artamkin
%T Action of biregular automorphisms of the affine plane on pairs of matrices
%J Izvestiya. Mathematics 
%D 1989
%P 433-439
%V 33
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1989_33_2_a12/
%G en
%F IM2_1989_33_2_a12
I. V. Artamkin. Action of biregular automorphisms of the affine plane on pairs of matrices. Izvestiya. Mathematics , Tome 33 (1989) no. 2, pp. 433-439. http://geodesic.mathdoc.fr/item/IM2_1989_33_2_a12/

[1] Huleck K., “On the classification of stable rank-$r$ vector bundles over the projective plane”, Proceedings of the Nice Conference 1979 on Vector Bundles and Differential Equations, Progress in Mathematics, 7, Birkhauser, 1980 | MR

[2] Shafarevisch I. R., “On some infinitedimensional groups”, Simposio Internazionale di Geometria Algebrica, Roma, 1967, 208–212

[3] Shafarevich I. R., “O nekotorykh beskonechnomernykh gruppakh, II”, Izv. AN SSSR. Ser. matem., 45:1 (1981), 214–226 | MR | Zbl