Email this article A canonical basis of a pair of compatible Poisson brackets on a matrix algebra
- Authors: Garazha A.A.1
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Affiliations:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Issue: Vol 211, No 6 (2020)
- Pages: 95-106
- Section: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/142358
- DOI: https://doi.org/10.4213/sm9282
- ID: 142358
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Abstract
Given an arbitrary complex matrix $A$ and a generic matrix $X$ we find a canonical basis for the Kronecker part of the bi-Lagrangian subspace with respect to the corresponding Poisson brackets on the Lie algebra $\mathfrak{gl}_n(\mathbb C)$, and also find a system of functions in bi-involution corresponding to this basis. In particular, for nilpotent matrices $A$ we prove that all nonzero functions obtained by applying the Mishchenko-Fomenko argument shift method to the coefficients of the characteristic polynomial form the Kronecker part of the complete system of functions in bi-involution. Bibliography: 9 titles.
About the authors
Aleksandra Andreevna Garazha
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Email: garazha.alex.andr@gmail.com
without scientific degree, no status
References
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