%0 Journal Article %A Bolsinov, Alexey %A Zhang, P. %D 2016 %T Jordan-Kronecker invariants of finite-dimensional Lie algebras %U https://repository.lboro.ac.uk/articles/journal_contribution/Jordan-Kronecker_invariants_of_finite-dimensional_Lie_algebras/9387938 %2 https://repository.lboro.ac.uk/ndownloader/files/17001167 %K untagged %K Mathematical Sciences not elsewhere classified %X 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. %I Loughborough University