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Jordan-Kronecker invariants of finite-dimensional Lie algebras
journal contribution
posted on 2016-01-05, 13:58 authored by Alexey BolsinovAlexey Bolsinov, P. ZhangFor 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.
Funding
This work was supported by the Ministry of Science and Education of Russia, grants no. 14.740.11.0876 and 11.G34.31.00
History
School
- Science
Department
- Mathematical Sciences
Citation
BOLSINOV, A.V. and ZHANG, P., 2016. Jordan-Kronecker invariants of finite-dimensional Lie algebras. Transformation Groups, 21(1), pp.51-86.Publisher
© SpringerVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2016Notes
The final publication is available at Springer via http://dx.doi.org/10.1007/s00031-015-9353-6ISSN
1083-4362eISSN
1531-586XPublisher version
Language
- en