Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systems

Abstract

We introduce the cotangent universal hierarchy that extends the so-called universal hierarchy (as for the latter, see e.g. arXiv:nlin/0202008, arXiv:nlin/0312043 and arXiv:nlin/0310036). Then we construct a (2+1)-dimensional double central extension of the cotangent universal hierarchy and show that this extension is bi-Hamiltonian. This yields, as a byproduct, the central extension of the original universal hierarchy.

12 pages, LaTeX 2e, minor changes (typos fixed, English improved, etc.)

References in corpus (3)

• Interpolating Dispersionless Integrable System
• Looped cotangent Virasoro algebra and non-linear integrable systems in dimension 2+1
• Multidimensional integrable systems and deformations of Lie algebra homomorphisms

Cited by in corpus (6)

• Classical R-matrix theory for bi-Hamiltonian field systems
• Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities
• The integrable heavenly type equations and their Lie-algebraic structure
• Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics
• A note on the Hyper--CR equation, and gauged $N=2$ supergravity
• Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras