Guha, Partha Moyal deformation of KdV and Virasoro action. (English) Zbl 1065.81070 J. Phys. Soc. Japan 73, No. 10, 2662-2666 (2004). Summary: The Lie algebra of pseudodifferential symbols \(\Psi D(S^1)\) on \(S^1\) has a natural Lie-Poisson structure. The Moyal deformation of dispersionless Korteweg-de Vries (KdV) equation is constructed from the action of Vect(\(S^1\)) on \(\Psi D(S^1\)). We also study the Moyal deformation of supersymmetric two-boson KdV equation. We offer their Lax representations. Using Souriau-Kravchenko-Khesin cocycle we are able to construct KdV equation. Cited in 2 Documents MSC: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations 81S10 Geometry and quantization, symplectic methods 53D55 Deformation quantization, star products Keywords:Moyal deformation; pseudodifferential symbols; Virasoro action; (nc)KdV PDFBibTeX XMLCite \textit{P. Guha}, J. Phys. Soc. Japan 73, No. 10, 2662--2666 (2004; Zbl 1065.81070) Full Text: DOI