On Integrability of the Kontsevich Non-Abelian ODE System |
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Authors: | Thomas Wolf Olga Efimovskaya |
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Affiliation: | (1) Laboratoire de Math?matiques, Informatique et Applications, Universit? de Haute Alsace, Mulhouse, France |
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Abstract: | We consider systems of ODEs with the right-hand side being Laurent polynomials in several non-commutative unknowns. In particular, these unknowns could be matrices of arbitrary size. An important example of such a system was proposed by M. Kontsevich (private communication). We prove the integrability of the Kontsevich system by finding a Lax pair, corresponding first integrals and commuting flows. We also provide a pre-Hamiltonian operator which maps gradients of integrals for the Kontsevich system to symmetries. |
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