Jordan-Kronecker invariants of finite-dimensional Lie algebras. (English) Zbl 1387.17011
Summary: For any finite-dimensional Lie algebra we introduce the notion of Jordan-Kronecker invariants, study their properties, and discuss examples. These invariants naturally appear in the framework of the bi-Hamiltonian approach to integrable systems on Lie algebras and are closely related to Mishchenko-Fomenko’s argument shift method. We also state a generalised argument shift conjecture and prove it for many series of Lie algebras.
References:
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