Journal of Lie Theory 18 (2008), No. 3, 595--600
Copyright Heldermann Verlag 2008
A Geometric Approach to the Frobenius Unicity Conjecture for the Markoff Equation
José M. Tornero
Departamento de Algebra, Facultad de Matemáticas, Universidad de Sevilla, P.O. 1160, 41080 Sevilla, Spain
tornero@us.es
The long-standing Frobenius conjecture on the unicity of ordered solutions for the Markoff equation is translated in a very simple way into an arithmetic statement on the existence of integral points on certain hyperbolas. Some previous work of Kang and Melville can then be used for relating the problem to a statement concerning rank 2 symmetric hyperbolic Kac-Moody algebras.
Keywords: Markoff equation, Frobenius unicity conjecture, integral points, hyperbolic Kac-Moody algebras, imaginary roots.
MSC: 11D09; 11D45, 14G05
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