Jordan-Kronecker invariants of finite-dimensional Lie algebras

2016-01-05T13:58:22Z (GMT) by Alexey Bolsinov P. Zhang
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 Mischenko–Fomenko’s argument shift method. We also state a generalised argument shift conjecture and prove it for many series of Lie algebras.