Journal of Lie Theory

no. 3
A Geometric Approach to the Frobenius Unicity Conjecture for the Markoff Equation
Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 595-600
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.
DOI: 10.5802/jolt.513
Classification: 11D09, 11D45, 14G05
Keywords: Markoff equation, Frobenius unicity conjecture, integral points, hyperbolic Kac-Moody algebras, imaginary roots 
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     author = {J. M. Tornero},
     title = {A {Geometric} {Approach} to the {Frobenius} {Unicity} {Conjecture} for the {Markoff} {Equation}},
     journal = {Journal of Lie Theory},
     pages = {595--600},
     year = {2008},
     volume = {18},
     number = {3},
     doi = {10.5802/jolt.513},
     zbl = {1163.11024},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.513/}
}
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J. M. Tornero. A Geometric Approach to the Frobenius Unicity Conjecture for the Markoff Equation. Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 595-600. doi: 10.5802/jolt.513

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