On limits of Mishchenko-Fomenko subalgebras in Poisson algebras of semisimple Lie algebras

DOI10.1023/A:1021713927119zbMath1022.17016OpenAlexW64687505MaRDI QIDQ1812455

V. V. Shuvalov

Publication date: 2002

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1021713927119

zbMATH Keywords

integrable Hamiltonian systemdegenerationsemisimple Lie algebrasPoisson algebrascommutative subalgebralimits of Mishchenko-Fomenko subalgebras

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Poisson algebras (17B63) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (13)

Finite-dimensional integrable systems: a collection of research problems ⋮ The argument shift method and the Gaudin model ⋮ Shift of argument algebras and de Concini–Procesi spaces ⋮ On the fibres of Mishchenko-Fomenko systems ⋮ Unnamed Item ⋮ Crystals and monodromy of Bethe vectors ⋮ Degeneration of Bethe subalgebras in the Yangian of \(\mathfrak {gl}_n\) ⋮ Limits of integrable Hamiltonians on semisimple Lie algebras ⋮ Limits of Gaudin algebras, quantization of bending flows, Jucys-Murphy elements and Gelfand-Tsetlin bases ⋮ On classical limits of Bethe subalgebras in Yangians ⋮ Gelfand-Tsetlin degeneration of shift of argument subalgebras in types B, C and D ⋮ Quantisation and nilpotent limits of Mishchenko–Fomenko subalgebras ⋮ Spectra of Bethe subalgebras of \(Y(\mathfrak{gl}_n)\) in tame representations

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