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Jordan-Kronecker invariants of finite-dimensional Lie algebras

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posted on 2016-01-05, 13:58 authored by Alexey BolsinovAlexey 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.

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

© Springer

Version

  • 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

2016

Notes

The final publication is available at Springer via http://dx.doi.org/10.1007/s00031-015-9353-6

ISSN

1083-4362

eISSN

1531-586X

Language

  • en

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