This article is cited in 4 papers

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.

UDC: 512.554.31+517.913

MSC: Primary 17B80; Secondary 17B45

Received: 22.03.2019 and 25.10.2019

DOI: 10.4213/sm9251

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

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