Verification of the generalized hypothesis of Mishchenko-Fomenko for Lie algebras of small dimension

DOI10.22405/2226-8383-2023-24-5-126-135MaRDI QIDQ6500275

Fedor Igorevich Lobzin

Publication date: 10 May 2024

Published in: Chebyshevskiĭ Sbornik (Search for Journal in Brave)

zbMATH Keywords

Lie-Poisson bracketcompatible Poisson bracketsets of polynomials in bi-involution

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Poisson algebras (17B63) Modular Lie (super)algebras (17B50)

Cites Work

• Jordan-Kronecker invariants of finite-dimensional Lie algebras
• A Proof of the Mishchenko-Fomenko Conjecture (1981)
• The Poisson center and polynomial, maximal Poisson commutative subalgebras, especially for nilpotent Lie algebras of dimension at most seven
• COMPATIBLE POISSON BRACKETS ON LIE ALGEBRAS AND COMPLETENESS OF FAMILIES OF FUNCTIONS IN INVOLUTION
• Invariants of real low dimension Lie algebras
• EULER EQUATIONS ON FINITE-DIMENSIONAL LIE GROUPS
• Open problems, questions and challenges in finite- dimensional integrable systems
• Complete sets of polynomials in bi-involution on nilpotent seven-dimensional Lie algebras

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