A family of the Poisson brackets compatible with the Sklyanin bracket
نویسندگان
چکیده
منابع مشابه
Compatible nonlocal Poisson brackets
In the present work, the integrable bi-Hamiltonian hierarchies related to compatible nonlocal Poisson brackets of hydrodynamic type are effectively constructed. For achieving this aim, first of all, the problem on the canonical form of a special type for compatible nonlocal Poisson brackets of hydrodynamic type is solved. The compatible pairs of nonlocal Poisson brackets of hydrodynamic type ha...
متن کاملFamily of Boundary Poisson Brackets
We find a new d-parameter family of ultra-local boundary Poisson brackets that satisfy the Jacobi identity. The two already known cases (hep-th/9305133, hep-th/9806249 and hepth/9901112) of ultra-local boundary Poisson brackets are included in this new continuous family as special cases. PACS number(s): 02.70.Pt, 11.10.Ef.
متن کاملCommutative Poisson subalgebras for the Sklyanin bracket and deformations of known integrable models
A hierarchy of commutative Poisson subalgebras for the Sklyanin bracket is proposed. Each of the subalgebras provides a complete set of integrals in involution with respect to the Sklyanin bracket. Using different representations of the bracket, we find some integrable models and a separation of variables for them. The models obtained are deformations of known integrable systems like the Goryac...
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چکیده ندارد.
15 صفحه اولAn operadic approach to deformation quantization of compatible Poisson brackets
An analogue of the Livernet–Loday operad for two compatible brackets, which is a flat deformation of the bi-Hamiltonian operad is constructed. The Livernet–Loday operad can be used to define ⋆-products and deformation quantization for Poisson structures. The constructed operad is used in the same way, introducing a definition of operadic deformation quantization of compatible Poisson structures...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2007
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/40/18/008