Algebraic proofs for shallow water bi-Hamiltonian systems for three cocycle of the semi-direct product of Kac-Moody and Virasoro Lie algebras

DOI10.1515/math-2018-0002zbMath1417.17031OpenAlexW2794313725WikidataQ113741070 ScholiaQ113741070MaRDI QIDQ1643965

Alexander Zuevsky

Publication date: 20 June 2018

Published in: Open Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/math-2018-0002

zbMATH Keywords

Verma modulescoadjoint orbitsbi-Hamiltonian systemsaffine Kac-Moody Lie algebras

Mathematics Subject Classification ID

Vertex operators; vertex operator algebras and related structures (17B69) Dynamical systems methods for problems in mechanics (70G60) Exactly solvable dynamic models in time-dependent statistical mechanics (82C23) Coadjoint orbits; nilpotent varieties (17B08)

Cites Work

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• Coadjoint orbits of the Virasoro group
• Generalizations of Virasoro group and Virasoro algebra through extensions by modules of tensor-densities on \(S^1\)
• Symplectic geometries on \(T^*\widetilde {G}\), Hamiltonian group actions and integrable systems
• Mathematics of dispersive water waves
• The geometry of the KdV equation
• Integrable Models
• Hamiltonian Structures on Coadjoint Orbits of Semidirect Product G = Diff+(S 1) ? < C ?(S 1, ?)