Nonlocal quadratic Poisson algebras, monodromy map, and Bogoyavlensky lattices
نویسندگان
چکیده
منابع مشابه
Nonlocal Quadratic Poisson Algebras, Monodromy Map, and Bogoyavlensky Lattices
A new Lax representation for the Bogoyavlensky lattice is found, its r–matrix interpretation is elaborated. The r–matrix structure turns out to be related to a highly nonlocal quadratic Poisson structure on a direct sum of asso-ciative algebras. The theory of such nonlocal structures is developed, the Poisson property of the monodromy map is worked out in the most general situation. Some proble...
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Discretizations of the Bogoyavlensky lattices are introduced, belonging to the same hierarchies as the continuous–time systems. The construction exemplifies the general scheme for integrable discretization of systems on Lie algebras with r–matrix Poisson brackets. An initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamilt...
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We exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial algebra R = C[X1, . . . , Xn] endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the semiclassical limit of the dualising bimodule for Hochschild homology of the corresponding quantum affine space. As a coro...
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This paper is mainly a review of the multi–Hamiltonian nature of Toda and generalized Toda lattices corresponding to the classical simple Lie groups but it includes also some new results. The areas investigated include master symmetries, recursion operators, higher Poisson brackets, invariants and group symmetries for the systems. In addition to the positive hierarchy we also consider the negat...
متن کاملTwisted Poincaré duality for some quadratic Poisson algebras
We exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial algebra R = C[X1, . . . , Xn] endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the semiclassical limit of the dualising bimodule for Hochschild homology of the corresponding quantum affine space. As a coro...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 1997
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.532090