BOLSINOV, A.V. and ZHANG, P., 2016. Jordan-Kronecker invariants of finite-dimensional Lie algebras. Transformation Groups, 21(1), pp.51-86.
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.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00031-015-9353-6
This work was supported by the Ministry of Science and Education of Russia, grants
no. 14.740.11.0876 and 11.G34.31.00