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Mat. Sb., 2020, Volume 211, Number 4, Pages 112–122 (Mi msb9251)  

Completeness of commutative Sokolov-Odesskii subalgebras and Nijenhuis operators on $\operatorname{gl}(n)$

A. Yu. Konyaev

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We prove the completeness of commutative subalgebras in the algebra $S(\operatorname{gl}(n))$ constructed from the algebraic Nijenhuis operators. The operators in question were proposed by Sokolov and Odesskii.
Bibliography: 17 titles.

Keywords: Lie algebras, integrable systems, algebraic Nijenhuis operators, Lie pencils.

Funding Agency Grant Number
Russian Science Foundation 17-11-01303
This research was supported by a grant of the Russian Science Foundation (project no. 17-11-01303).


DOI: https://doi.org/10.4213/sm9251

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English version:
Sbornik: Mathematics, 2020, 211:4, 583–593

Bibliographic databases:

UDC: 512.554.31+517.913
MSC: Primary 17B80; Secondary 17B45
Received: 22.03.2019 and 25.10.2019

Citation: A. Yu. Konyaev, “Completeness of commutative Sokolov-Odesskii subalgebras and Nijenhuis operators on $\operatorname{gl}(n)$”, Mat. Sb., 211:4 (2020), 112–122; Sb. Math., 211:4 (2020), 583–593

Citation in format AMSBIB
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