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- W3016918574 abstract "Abstract Given an arbitrary complex matrix <?CDATA $A$?> and a generic matrix <?CDATA $X$?> 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 <?CDATA $mathfrak{gl}_n(mathbb C)$?> , and also find a system of functions in bi-involution corresponding to this basis. In particular, for nilpotent matrices <?CDATA $A$?> 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." @default.
- W3016918574 created "2020-04-24" @default.
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- W3016918574 date "2020-06-01" @default.
- W3016918574 modified "2023-09-23" @default.
- W3016918574 title "A canonical basis of a pair of compatible Poisson brackets on a matrix algebra" @default.
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- W3016918574 doi "https://doi.org/10.1070/sm9282" @default.
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