\(W\)-algebras and the equivalence of bihamiltonian, Drinfeld-Sokolov and Dirac reductions

DOI10.1016/j.geomphys.2014.06.003zbMath1304.37045arXiv0911.2116OpenAlexW2963684288MaRDI QIDQ2250963

Yassir Ibrahim Dinar

Publication date: 22 July 2014

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.2116

zbMATH Keywords

\(W\)-algebraSlodowy sliceDirac reductionDrinfeld-Sokolov reductiontransverse Poisson structurebi-Hamiltonian reduction

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) 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) Poisson algebras (17B63) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (max. 100)

Low-dimensional bihamiltonian structures of topological type ⋮ Dirac reductions and classical W-algebras ⋮ Poisson pencils: reduction, exactness, and invariants ⋮ The WDVV solution \(E_8(a_1)\) ⋮ Algebraic classical \(W\)-algebras and Frobenius manifolds ⋮ On integrability of transverse Lie-Poisson structures at nilpotent elements ⋮ Affine Kac-Moody algebras and tau-functions for the Drinfeld-Sokolov hierarchies: the matrix-resolvent method ⋮ Boussinesq hierarchy and bi-Hamiltonian geometry

Cites Work

• Frobenius manifolds from regular classical \(W\)-algebras
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• Reduction of Poisson manifolds
• Generalized Drinfel'd-Sokolov hierarchies
• Generalized Toda theories and \(\mathcal W\)-algebras associated with integral gradings
• Drinfeld-Sokolov reduction on a simple Lie algebra from the bihamiltonian point of view
• Bihamiltonian reductions and \({\mathcal W}_n\)-algebras
• On the completeness of the set of classical \({\mathcal W}\)-algebras obtained from DS reductions
• Lectures on classical \(W\)-algebras
• Generalized Drinfel'd-Sokolov hierarchies. II: The Hamiltonian structures
• Special transverse slices and their enveloping algebras
• Equivalence of the Drinfeld-Sokolov reduction to a bi-Hamiltonian reduction
• Nilpotent orbits and finite W-algebras
• Good grading polytopes
• Regular conjugacy classes in the Weyl group and integrable hierarchies
• A note on fractional KdV hierarchies
• Frobenius Manifolds from Subregular Classical W-algebras
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