Titlebook: Recent Developments in Integrable Systems and Related Topics of Mathematical Physics; Kezenoi-Am, Russia, Victor M. Buchstaber,Sotiris Kon

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Survey of the Deformation Quantization of Commutative Families,xtension of a Poisson-commutative subalgebra in . (where . is a Poisson manifold) to a commutative subalgebra in the deformation quantization of ., the algebra .. A case of particular interest, which we consider with certain detail is the situation, when . and the commutative subalgebra is construct

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Introduction,d monographs in the literature where all the necessary definitions and constructions can be found. Here, we indicate the interrelationships between several research directions in this field of science that until recently were regarded as independent and distant from each other

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Quadro-Cubic Cremona Transformations and Feigin-Odesskii-Sklyanin Algebras with 5 Generators,Poisson tensors on .. For the Sklyanin algebras . and ., we explicitly write the Poisson morphisms on the moduli space of the vector bundles on the normal elliptic curve . in ., studied by Polishchuk and Odesskii-Feigin as the quadro-cubic Cremona transformation on ..

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Graded Thread Modules Over the Positive Part of the Witt (Virasoro) Algebra,f two multiplicative generators . of . as . and . for . and . are two arbitrary constants (.)..We classify .-dimensional graded thread .-modules of three important types for sufficiently large .. New examples of graded thread .-modules different from finite-dimensional quotients of . and . are found.