题  目：Poisson algebras and Jacobi pairs

报告人：苏育才教授   上海同济大学数学学院

时  间：2012年2月23日下午3：00--4:00
地  点：管理科研楼1518

摘  要：In this talk, we discuss the natural Poisson algebra structure (P,[.,.],.) on the space P = C[y]((x^{-1/N})) for some sufficient large N, and introduce some automorphisms of P which are products of the automorphisms of forms e^{ad_H}. These automorphisms are used to study some properties of Jacobi pairs in P. In particular, starting from a Jacobi pair (F,G) in C[x,y] which violates the two-dimensional Jacobian conjecture, by applying some variable changes,  we obtain a pair still denoted by (F,G) in C[x^{/pm1/N},y] with the form F=x^{m/(m+n)}(f+F_0), G=x^{n/(m+n)}(g+G_0) for some positive integers m,n, and f,g in C[y], F_0,G_0 in x^{-1/N} C[x^{-1/N},y], such that F,G satisfy some additional conditions. We also generalize some results to the Weyl algebra W = C[v]((u^{-1/N})) with relation [u,v] = 1, and obtain some properties of pairs (F,G) satisfying [F,G] = 1, referred to as Dixmier pairs.

主办单位：数学科学学院     中科院吴文俊数学重点实验室

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