Algebraic Properties of the Semi-direct Product of Kac–Moody and Virasoro Lie Algebras and Associated Bi-Hamiltonian Systems

DOI10.1007/978-3-319-32857-7_1zbMath1403.17027OpenAlexW2517278407MaRDI QIDQ2954404

Alexander Zuevsky

Publication date: 13 January 2017

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-32857-7_1

zbMATH Keywords

coadjoint orbitsVirasoro algebrasemi-direct productbi-Hamiltonian systemsCasimir functionsaffine Kac-Moody Lie algebraassociated Verma modules

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Virasoro and related algebras (17B68) Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics (37K65)

Cites Work

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• Coadjoint orbits of the Virasoro group
• Symplectic geometries on \(T^*\widetilde {G}\), Hamiltonian group actions and integrable systems
• Mathematics of dispersive water waves
• The geometry of the KdV equation

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