Abstract
We construct a large family of Hamiltonian systems which are connected with root systems of complex simple Lie algebras. These systems are generalizations of the KM system. The Hamiltonian vector field is homogeneous cubic but in a number of cases a simple change of variables transforms such a system to a quadratic Lotka–Volterra system. We classify all possible Lotka–Volterra systems that arise via this algorithm in the A n case.
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Acknowledgements
The first author was supported by a University of Cyprus Postdoctoral fellowship. The work of the third author was co-funded by the European Regional Development Fund and the Republic of Cyprus through the Research Promotion Foundation (Project: PENEK/0311/30).
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Charalambides, S.A., Damianou, P.A., Evripidou, C.A. (2014). A Construction of Generalized Lotka–Volterra Systems Connected with \(\mathfrak{s}\mathfrak{l}_{n}(\mathbb{C})\) . In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 111. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55285-7_23
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DOI: https://doi.org/10.1007/978-4-431-55285-7_23
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