This article is cited in 2 papers

Complete sets of polynomials in bi-involution on nilpotent seven-dimensional Lie algebras

K. S. Vorushilov

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

Abstract: In this paper, we construct complete sets of polynomials in bi-involution on nilpotent Lie algebras of dimension 7 in the list due to Gong. Thus we verify the generalized Mishchenko-Fomenko conjecture for all algebras in this list.
Bibliography: 14 titles.

Keywords: Lie algebras, integrable Hamiltonian systems, complete commutative sets of polynomials, argument shift method.

UDC: 514.745.8

MSC: Primary 30C65, 30L10, 58C06; Secondary 31C12, 31C15, 31B15, 30D45

Received: 01.09.2020 and 15.02.2021

DOI: 10.4213/sm9501

 English version: Sbornik: Mathematics, 2021, 212:9, 1193–1207

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