L'interprétation matricielle de la théorie de Markoff classique

Serge Perrine

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 32, 1-70

Abstract:

On explicite l'approche de Cohn (1955) de la théorie de Markoff. On montre en particulier comment l'arbre complet des solutions de l'équation diophantienne associée apparasît comme quotient du groupe GL ( 2 , ℤ ) des matrices 2 × 2 à coefficients entiers et de déterminant ± 1 par un sous-groupe diédral D 6 à 12 éléments. Différents développements intermédiaires sont faits autour du groupe Aut ( F 2 ) des automorphismes du groupe libre engendré par deux éléments F 2 .

We detail the approach followed by Cohn for the Markoff theory. We show particularly how appears the whole tree of solutions for the associated Diophantine equation as a quotient of the group GL ( 2 , ℤ ) of matrices 2 × 2 with integer coefficients and determinant ± 1 by its dihedral subgroup D 6 with 12 elements. Some developments are made with the group Aut ( F 2 ) of automorphisms of the free group F 2 generated by two elements.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:854739

DOI: 10.1155/S0161171202012875

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